Supergravity

We construct the Killing(-Yano) tensors for a large class of charged black holes in higher dimensions and study general properties of such tensors, in particular, their behavior under string dualities. Killing(-Yano) tensors encode the symmetries beyond isometries, which lead to insights into dynamics of particles and fields on a given geometry by providing a set of conserved quantities. By analyzing the eigenvalues of the Killing tensor, we provide a prescription for constructing several conserved quantities starting from a single object, and we demonstrate that Killing tensors in higher dimensions are always associated with ellipsoidal coordinates. We also determine the transformations of the Killing(-Yano) tensors under string dualities, and find the unique modification of the Killing-Yano equation consistent with these symmetries. These results are used to construct the explicit form of the Killing(-Yano) tensors for the Myers-Perry black hole in arbitrary number of dimensions and for its charged version.

This thesis compiles the results of six works which deal with - inflationary model building and estimation of cosmological parameters from various field theoretic setup, quantification of reheating temperature, studies of leptogenesis in braneworld and estimation of primordial non-Gaussianity from ${\cal N}=1$ supergravity using $\delta N$ formalism.

We start our discussion with exploring the possibility of
MSSM inflation in the light of recent observed data from various D -flat directions using the saddle and inflection point techniques. The effective inflaton potential around saddle point and inflection point have been utilized in estimating the observable parameters and confronting them with WMAP7 and Planck dataset.


Next we explore the possibility of inflation from the five dimensional ${\cal N}=2$ supergravity setup by deriving the effective potential in the context of Randall-Sundrum like braneworld model and Dirac Bonn Infeld Galileon. After deriving an four dimensional effective potential, we obtain the inflationary observables from both the scenarios and confront them with the  WMAP7 data. Further we fit the CMB angular power spectra from TT anisotropy and other polarization data obtained from WMAP7.

Further, we discuss the non-trivial features of reheating from supergravity inspired braneworld model, where the results are to some extent different from that of the usual low energy General Relativistic counterpart, because of the modified Friedmann equations in this setup. We explicitly derive the analytical expressions for the reheating temperature and further solve the evolution equation of the number density of thermal gravitino which results in the gravitino abundance.


Finally, we study the primordial non-Gaussian features using $\delta N$ formalism of unavoidable higher dimensional non-renormalizable K\"ahler operators for ${\cal N}=1$ supergravity framework.In particular we study the nonlinear evolution of cosmological perturbations on large scales which enable us to compute the curvature perturbation,  without solving the exact perturbed field equations.Hence we compute the various non-Gaussian parameters for local type of non-Gaussianities,
for a generic class of sub-Planckian models dominated by the Hubble-induced corrections.

In this thesis, consisting of two main parts, we study observational signatures of cosmic (super)strings in the context of D-brane inflation and properties of scalar perturbations on generic homogeneous inflating backgrounds. In the first part we study the production, nature and decay processes of cosmic superstrings in two widely used effective models of D-brane inflation, namely the $D3/D7$ and $D3/\bar{D}3$ models. Specifically, we show that the strings produced in $D3/D7$ are of local axionic type and we place constraints on the tension while arguing that the supersymmetry breaking mechanism of the model needs to be altered according to supergravity constraints on constant Fayet-Iliopoulos terms. Moreover, we study radiative processes of cosmic superstrings on warped backgrounds. We argue that placing the string formation in a natural context such as $D3/\bar{D}3$ inflation, restricts the forms of possible radiation from these objects. Motivated by these string models, which inevitably result in the presence of heavy moduli fields during inflation, in the second part, using the Effective Field Theory (EFT) of inflation, we construct operators that capture the effects of massive scalars on the low energy dynamics of inflaton perturbations. We compute the energy scales that define the validity window of the EFT such as the scale where ultra violet (UV) degrees of freedom become operational and the scale where the EFT becomes strongly coupled. We show that the low energy operators related to heavy fields induce a dispersion relation for the light modes admitting two regimes: a linear and a non linear/dispersive one. Assuming that these modes cross the Hubble scale within the dispersive regime, we compute observables related to two- and three-point correlators and show how they are directly connected with the scale of UV physics.

We review the major mathematical concepts involved in the dimensional reduction of D=11 N=1 supergravity theory over a Calabi-Yau manifold with non-trivial complex structure moduli resulting in ungauged D=5 N=2 supergravity theory with hypermultiplets. This last has a particularly rich structure with many underlying geometries. We reproduce the entire calculation and particularly emphasize its symplectic symmetry and how that arises from the topology of the underlying subspace. The review is intended to fill in a specific gap in the literature with the hope that it would be useful to both the beginner and the expert alike.

A discussion of String Theory highlighting some key historical steps, the main achievements and some of the main open questions. Most of the presentation is aimed at the general public, but graduate students will be able to get more details from a careful reading.

In this work, we have developed an elegant algorithm to study the cosmological consequences from a huge class of quantum field theories (i.e. superstring theory, supergrav-ity, extra dimensional theory, modified gravity etc.), which are equivalently described by soft attractors in the effective field theory framework. In this description we have restricted our analysis for two scalar fields-dilaton and Higgsotic fields minimally coupled with Einstein gravity, which can be generalized for any arbitrary number of scalar field contents with generalized non-canonical and non-minimal interactions. We have explicitly used R 2 gravity, from which we have studied the attractor and non-attractor phase by exactly computing two point, three point and four point correlation functions from scalar fluctuations using In-In (Schwinger-Keldysh) and δN formalism. We have also presented theoretical bounds on the amplitude, tilt and running of the primordial power spectrum, various shapes (equilateral, squeezed, folded kite or counter collinear) of the amplitude as obtained from three and four point scalar functions, which are consistent with observed data. Also the results from two point tensor fluctuations and field excursion formula are explicitly presented for attractor and non-attractor phase. Further, reheating constraints, scale dependent behaviour of the couplings and the dynamical solution for the dilaton and Higgsotic fields are also presented. New sets of consistency relations between two, three and four point observables are also presented, which shows significant deviation from canonical slow roll models. Additionally, three possible theoretical proposals have presented to overcome the tachyonic instability at the time of late time acceleration. Finally, we have also provided the bulk interpretation from the three and four point scalar correlation functions for completeness.

This paper is fundamentally a review, a thesis, of principal results obtained in some sectors of Number Theory and String Theory of various authoritative theoretical physicists and mathematicians. Precisely, we have described some mathematical results regarding the Fermat's Last Theorem, the Mellin transform, the Riemann zeta function, the Ramanujan's modular equations, how primes and adeles are related to the Riemann zeta functions and the p-adic and adelic string theory. Furthermore, we show that also the fundamental relationship concerning the Palumbo-Nardelli model (a general relationship that links bosonic string action and superstring action, i.e. bosonic and fermionic strings in all natural systems), can be related with some equations regarding the p-adic (adelic) string sector. Thence, in conclusion, we have described some new interesting connections that are been obtained between String Theory and Number Theory, with regard the arguments above mentioned. In the Chapters 1 and 2, we have described the mathematics concerning the Fermat's Last Theorem, precisely the Wiles approach in the Chapter 1 and further mathematical aspects concerning the Fermat's Last Theorem, precisely the modular forms, the Euler products, the Shimura map and the automorphic L-functions in the Chapter 2. Furthermore. In this chapter, we have described also some mathematical applications of the Mellin transform, only mentioned in the Chapter 1, the zeta-function quantum field theory and the quantum L-functions. In the Chapter 3, we have described how primes and adeles are related to the Riemann zeta function, precisely the Connes approach. In the Chapter 4, we have described the p-adic and adelic strings, precisely the open and closed p-adic strings, the adelic strings, the solitonic q-branes of padic string theory and the open and closed scalar zeta strings. In the Chapter 5, we have described some correlations obtained between some solutions in string theory, Riemann zeta function and Palumbo-Nardelli model. Precisely, we have showed the cosmological solutions from the D3/D7 system, the classification and stability of cosmological solutions, the solution applied to ten dimensional IIB supergravity, the connections with some equations concerning the Riemann zeta function, the Palumbo-Nardelli model and the Ramanujan's identities. Furthermore, we have described the interactions between intersecting D-branes and the general action and equations of motion for a probe D3-brane moving through a type IIB supergravity background. Finally, in the Chapter 6, we have showed the connections between the equations of the various chapters.

UPDATED AND REVISITED VERSION - 05.11.2021

Consciousness is considered as a fundamental property of the universe in quantum theories of consciousness. We consider our physical universe as appeared by the phase-like transition of the energy waves, unfolded from 10 dimensions. The human brain and its mental aspects are associated with classical brain physiology and are also part of a quantum physical universe. We consider the whole universe being multi-dimensional, of (4 + D)-dimensional Friedmann-Robertson-Walker-type (FRW), with complex scale factor “R + i RI”, where “R” is the scale factor corresponding to the usual 4-dimensional universe, and “i RI” is that of D-dimensional space-time. It is found that for D = 6 (i.e. in 10 dimensions), the Wheeler-DeWitt equation is symmetric under the exchange RI ↔ R. Mathematically, when D = 6, it is RI = R and the physical universe starts. The universe starts with the symmetry breaking of group SU(11). We assume that the extra-dimensions “D” are associated with a mental-consciousness or that of the individual mind-consciousness is (partly) an expression of a universal mind-consciousness through holonomic communication with quantum fields. “Consciousness” is created by the electromagnetic force in the framework of SU(6) U(1), whereas “mind” is created by the framework of SU(2)  U(1). The human brain is conceived as an interfacing organ that not only produces mind and consciousness, but also receives information. The brain or parts of it are conceived as an “interference hologram” of incoming data and already existing ones (a “personal universe”), equivalent to the subject’s memory. If properly analyzed, information about the outer world can be distilled, with the analyzer being cerebral electrophysiology.

In this paper my prime objective is to analyze the constraints on a sub-Planckian excursion of a single inflaton field within Effective Field Theory framework in a model independent fashion. For a generic single field inflationary potential, using the various parameterization of the primordial power spectrum I have derived the most general expression for the field excursion in terms of various inflationary observables, applying the observational constraints obtained from recent Planck 2015 and Planck 2015 +BICEP2/Keck Array data. By explicit computation I have reconstructed the structural form of the inflationary potential by constraining the Taylor expansion coefficients appearing in the generic expansion of the potential within the Effective Field Theory. Next I have explicitly derived, a set of higher order inflationary consistency relationships, which would help us to break the degeneracy between various class of inflationary models by differentiating them. I also provided two simple examples of Effective Theory of inflation- inflection-point model and saddle-point model to check the compatibility of the prescribed methodology in the light of Planck 2015 and Planck 2015 +BICEP2/Keck Array data. Finally, I have also checked the validity of the prescription by estimating the cosmological parameters and fitting the theoretical CMB TT, TE and EE angular power spectra with the observed data within the multipole range 2<l<2500.

The presence of RR and NS three-form fluxes in type IIB string compactification on a Calabi-Yau orientifold gives rise to a nontrivial superpotential W for the dilaton and complex structure moduli. This superpotential is computable in terms of the period integrals of the Calabi-Yau manifold. In this paper, we present explicit examples of both supersymmetric and nonsupersymmetric solutions to the resulting 4d Script N = 1 supersymmetric no-scale supergravity, including some nonsupersymmetric solutions with relatively small values of W. Our examples arise on orientifolds of the hypersurfaces in WP41,1,1,1,4 and WP41,1,2,2,6. They serve as explicit illustrations of several of the ingredients which have played a role in the recent proposals for constructing de Sitter vacua of string theory.

We describe in detail the derivation of a superconformal off-shell formulation of the alternative N=2, d=5 ungauged supergravity of Nishino and Rajpoot, coupled to n Abelian vector multiplets, using a general dilaton-Weyl multiplet. We generalize the vector multiplet coupling available in the literature and show under which assumptions that the scalar manifold reduces to the known case of SO(1,1) × SO(1,n)/SO(n). As an application of the formalism we propose generalized vector multiplet coupled higher curvature terms, whose construction we sketch briefly.

In this paper I provide a general framework based on $\delta N$ formalism to study the features of unavoidable higher dimensional non-renormalizable K\"ahler operators for ${\cal N}=1$ supergravity (SUGRA) during primordial inflation from the combined constraint on non-Gaussianity, sound speed and CMB dipolar asymmetry as obtained from the recent Planck data.
In particular I study the nonlinear evolution of cosmological perturbations on large scales which enables us to compute the curvature perturbation, $\zeta$, without solving the exact perturbed field equations. Further I compute the non-Gaussian parameters $f_{NL}$ , $\tau_{NL}$ and $g_{NL}$ for local type of non-Gaussianities and CMB dipolar asymmetry parameter, $ A_{CMB}$, using the $\delta N$ formalism  for a generic class of sub-Planckian models induced by the Hubble-induced corrections for a minimal supersymmetric D-flat direction where inflation occurs at the point of inflection within the visible sector.
Hence by using multi parameter scan I constrain the non-minimal couplings appearing in non-renormalizable K\"ahler operators within, ${\cal O}(1)$, for the speed of sound, $0.02\leq c_s\leq 1$, and tensor to scalar, $10^{-22} \leq r_{\star} \leq 0.12$. Finally applying all of these constraints I will fix the lower as well as the upper bound of the non-Gaussian parameters within, ${\cal O}(1-5)\leq f_{NL}\leq 8.5$, ${\cal O}(75-150)\leq\tau_{NL}\leq 2800$ and ${\cal O}(17.4-34.7)\leq g_{NL}\leq 648.2$, and CMB dipolar asymmetry parameter within the range, $0.05\leq A_{CMB}\leq 0.09$.

We introduce a model of potential driven DBI Galileon inflation in background N=1,D=4 SUGRA. Starting from D4-$\bar{D4}$ brane-antibrane in the bulk N=2,D=5 SUGRA including quadratic Gauss-Bonnet corrections, we derive an effective N=1,D=4 SUGRA by dimensional reduction, that results in a Coleman-Weinberg type Galileon potential. We employ this potential in modeling inflation and in subsequent study of primordial quantum fluctuations for scalar and tensor modes. Further, we estimate the major observable parameters in both de Sitter (DS) and beyond de Sitter (BDS) limits and confront them with recent observational data from WMAP7 by using the publicly available code CAMB.

We study the large volume limit of the scalar potential in Calabi-Yau flux compactifications of type IIB string theory. Under general circumstances there exists a limit in which the potential approaches zero from below, with an associated non-supersymmetric AdS minimum at exponentially large volume. Both this and its de Sitter uplift are tachyon-free, thereby fixing all Kahler and complex structure moduli, which has been difficult to achieve in the KKLT scenario. Also, for the class of vacua described in this paper, the gravitino mass is independent of the flux discretuum, whereas the ratio of the string scale to the 4d Planck scale is hierarchically small but flux dependent. The inclusion of alpha' corrections plays a crucial role in the structure of the potential. We illustrate these ideas through explicit computations for a particular Calabi-Yau manifold.

This review is devoted to some aspects of non–linear Supersymmetry in four dimensions that can be efficiently described via nilpotent superfields, in both rigid and curved Superspace. Our focus is mainly on the partial breaking of rigid N = 2 Supersymmetry and on a class of generalized Born–Infeld systems that originate from Special Geometry and on some prototype cosmological models, starting from the Supergravity embedding of Starobinsky
inflation. However, as an aside we also review briefly some interesting two–field extensions
of the Born–Infeld Lagrangian whose field equations enjoy extended duality symmetries.

In this revisited research thesis, we calculate some Ramanujan expressions concerning the "First letter to Hardy". We describe the possible mathematical connections with some equations and topics concerning the Supersymmetry Breaking, Nilpotent Supergravity and Pre-Inflationary Clues.

v2  -  REVISITED VERSION  -  14.03.2021

We attempt to reconcile seemingly conflicting experimental results on the Higgs boson mass, the anomalous magnetic moment of the muon, null results in search for supersymmetry at the LHC within the 8 TeV data and results from B-physics, all within the context of supersymmetric grand unified theories. Specifically, we consider a supergravity grand unification model with non-universal gaugino masses where we take the SU(3)C gaugino field to be much heavier than the other gaugino and sfermion fields at the unification scale. This construction naturally leads to a large mass splitting between the slepton and squark masses, due to the mass splitting between the electroweak gauginos and the gluino. The heavy Higgs bosons and Higgsinos also follow the gluino toward large masses. We carry out a Bayesian Monte Carlo analysis of the parametric space and find that it can simultaneously explain the large Higgs mass, and the anomalous magnetic moment of the muon, while producing a negligible correction to the Standard Model prediction for Br(B0s→μ+μ−). We also find that the model leads to an excess in the Higgs diphoton decay rate. A brief discussion of the possibility of detection of the light particles is given. Also discussed are the implications of the model for dark matter.

We derive an exact expression for the Fourier coefficients of elliptic genera of Calabi-Yau manifolds. When applied to k-fold symmetric products of K3 surfaces the expression is well-suited to studying the AdS/CFT correspondence on AdS3 x S3. The expression also elucidates an SL(2,Z) invariant phase diagram for the D1/D5 system involving deconfining transitions in the limit as k goes to infinity.

In this research thesis, we describe various equations concerning the Volkov-Akulov-Starobinsky supergravity. We obtain new possible mathematical connections with several parameters of Number Theory and String Theory.


Below the link of some papers related to this work:



https://www.academia.edu/50214087/
https://www.academia.edu/50300304/
https://www.academia.edu/50347733/

Abdus Salam was a true master of 20th Century Theoretical Physics. Not only was he a pioneer of the Standard Model (for which he shared the Nobel Prize with S. Glashow and S. Weinberg), but he also (co)authored many other outstanding contributions to the field of Fundamental Interactions and their unification. In particular, he was a major contributor to the development of supersymmetric theories, where he also coined the word "Supersymmetry" (replacing the earlier "Supergauges" drawn from String Theory). He also introduced the basic concept of "Superspace" and the notion of "Goldstone Fermion" (Goldstino). These concepts proved instrumental for the exploration of the ultraviolet properties and for the study of spontaneously broken phases of super Yang-Mills theories and Supergravity. They continue to play a key role in current developments in Early-Universe Cosmology. In this contribution we review models of inflation based on Supergravity with spontaneously broken local supersymmetry, with emphasis on the role of nilpotent superfields to describe a de Sitter phase of our Universe.

We present a complete explicit N=1, d=4 supergravity action in an arbitrary Jordan frame with non-minimal scalar-curvature coupling of the form $\Phi(z, \bar z)\, R$. The action is derived by suitably gauge-fixing the superconformal action. The theory has a modified Kaehler geometry, and it exhibits a significant dependence on the frame function $\Phi (z, \bar z)$ and its derivatives over scalars, in the bosonic as well as in the fermionic part of the action. Under certain simple conditions, the scalar kinetic terms in the Jordan frame have a canonical form. We consider an embedding of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) gauge theory into supergravity, clarifying the Higgs inflation model recently proposed by Einhorn and Jones. We find that the conditions for canonical kinetic terms are satisfied for the NMSSM scalars in the Jordan frame, which leads to a simple action. However, we find that the gauge singlet field experiences a strong tachyonic instability during inflation in this model. Thus, a modification of the model is required to support the Higgs-type inflation.