The Journal of high energy physics/The journal of high energy physics, May 24, 2024
We construct a model of Pauli spin operators with all-to-all 4-local interactions by replacing Ma... more We construct a model of Pauli spin operators with all-to-all 4-local interactions by replacing Majorana fermions in the SYK model with spin operators. Equivalently, we replace fermions with hard-core bosons. We study this model numerically and compare the properties with those of the SYK model. We observe a striking quantitative coincidence between the spin model and the SYK model, which suggests that this spin model is strongly chaotic and, perhaps, can play some role in holography. We also discuss the path-integral approach with multi-local fields and the possibility of quantum simulations. This model may be an interesting target for quantum simulations because Pauli spins are easier to implement than fermions on qubit-based quantum devices.
We explore the question of finiteness of the entanglement entropy in gravitational theories whose... more We explore the question of finiteness of the entanglement entropy in gravitational theories whose emergent space is the target space of a holographic dual. In the well studied duality of two-dimensional non-critical string theory and c = 1 matrix model, this question has been studied earlier using fermionic many-body theory in the space of eigenvalues. The entanglement entropy of a subregion of the eigenvalue space, which is the target space entanglement in the matrix model, is finite, with the scale being provided by the local Fermi momentum. The Fermi momentum is, however, a position-dependent string coupling, as is clear in the collective field theory formulation. This suggests that the finiteness is a non-perturbative effect. We provide evidence for this expectation by an explicit calculation in the collective field theory of matrix quantum mechanics with vanishing potential. The leading term in the cumulant expansion of the entanglement entropy is calculated using exact eigenstates and eigenvalues of the collective Hamiltonian, yielding a finite result, in precise agreement with the fermion answer. Treating the theory perturbatively, we show that each term in the perturbation expansion is UV divergent. However the series can be resummed, yielding the exact finite result. Our results indicate that the finiteness of the entanglement entropy for higher dimensional string theories is non-perturbative as well, with the scale provided by the Newton constant. Dedicated to the memory of Ivan Andrić.
We extend the operator construction given by us earlier (for bosonic strings) to the Neveu-Schwar... more We extend the operator construction given by us earlier (for bosonic strings) to the Neveu-Schwarz-Ramond (NSR) superstrings. Witten's approach to interactions is followed. A construction of the interaction vertex for NS-NS-NS and NS-R-R string-states is given. The associated ghost interactions and the integration operator are also constructed explicitly. The field theory is formulated not only in the "bosonized" representation but also in the fundamental ghost representation. This allows a systematic expansion in terms of local fields.
We discuss the large N expansion in backgrounds of extended states with focus on implementation o... more We discuss the large N expansion in backgrounds of extended states with focus on implementation of Goldstone symmetries and the construction of the associated Hilbert space. The formulation is given in the general framework of collective field theory. Case of translational symmetry is described first, as the basic example. The large N thermofield represents the main topics, with the emergent dynamics of Left-Right bulk fields and collective symmetry coordinates. These give the basis for a 1/N expansion. Dedicated to the memory of Jean-Loup Gervais.
Springer proceedings in mathematics & statistics, 2018
In this article, starting from a review of basic aspects of the Sachdev-Ye-Kitaev (SYK) model in ... more In this article, starting from a review of basic aspects of the Sachdev-Ye-Kitaev (SYK) model in the large N limit, we discuss at non-linear-level the deduction of the zero mode effective Schwarzian action, featuring emergent finite reparametrization symmetry. We then discuss the question of identifying the bulk space-time of the SYK model. We explain the need for non-local (Radon-type) transformations on external legs of n-point Green’s functions, leading to a dual theory with Euclidean AdS signature with additional leg-factors. We show that the SYK spectrum and the bi-local propagator can be obtained from a Horava-Witten type compactification of a three dimensional model.
Progress in understanding and solving a large class of two-dimensional nonlinear quantum field th... more Progress in understanding and solving a large class of two-dimensional nonlinear quantum field theories is reviewed. The discovery and development of the inverse scattering method for solving partial differential equations, and development of new perturbative methods are discussed. The generalized Bethe-ansatz method and its application to exactly diagonalize a fermionic problem are covered. 52 references. (GHT)
The main emphasis in the theoretical program has been in the area of string theory; also investig... more The main emphasis in the theoretical program has been in the area of string theory; also investigated were confinement and other aspects of QCD, electroweak symmetry breaking, and electroweak baryogenesis. The research program in computational physics concentrated on the development of the source Galerkin method of numerical quantum field theory. One portion of the experimental program dealt with interactions of leptons and hadrons from accelerator and strophysics sources. A description of the Large Volume Detector at Gran Sasso and its use as a stellar collapse monitor is given, along with an account of research and development on resistive plate counters. The rest of the experimental program concerns hadron collider and neutrino physics, with major emphasis on the D0 experiment at the Tevatron. The commissioning of the D0 detector and its operation are described, along with D0 analysis. Also reported is a novel cryogenic technique utilizing superfluid helium for neutrino calorimetry.
We discuss point canonical transformations using the path integral quantization procedure. First,... more We discuss point canonical transformations using the path integral quantization procedure. First, employing the Feynman diagram technique we demonstrate how a formal treatment of point transformations leads to erroneous results. Then we present the correct treatment of this problem using a more precise definition of path integrals. We show how this more careful treatment leads to additional potential terms in the action as compared to the formal treatment. We also demonstrate the equivalence of our results with the corresponding operator method discussion. Furthermore, we investigate the consequences of these results on the path integral collective coordinate method. Giving the improved treatment on the one-soliton sector example we establish the path integral collective coordinate method of the same level of rigor as the parallel operator approaches.
We review two approaches to string dynamics: the renormalization group method and the string fiel... more We review two approaches to string dynamics: the renormalization group method and the string field theory formalism. The emphasis is on the relationship between these two seemingly different methods. The basic line of thought is that a renormalization group flow of a most general background coupled σ-model should lead to the equations of string field theory. Recent progress on this is summarized and a critical review of the results is given. Some new ideas concerning most general couplings are described.
We present an investigation of quantum fluctuations about pseudoparticle solutions in the two-dim... more We present an investigation of quantum fluctuations about pseudoparticle solutions in the two-dimensional a-model First, for the one pseudoparticle case, we solve the small oscillation problem and compute the first quantum correction to the classical result. In the two-pseudoparticle case, we transform the small oscillation problem into an ordinary Schrbdmger equation with an interaction depending on distance between the pseudo particles. We are then able to sclve the limiting cases of zero and infinite separations-NOTICE-This report was prepared as an account of work sponsored by the United States Government Neither the United States nor the United States Energy Research and Development Administration, nor any of their employees, nor any of their contractors subcontractors, or their employees makes any warranty express or implied, or assumes any legal liability or responsibility Tor the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights Research sponsored by_ the Energy Research and Development Administration, Grant No E(ll-l)-2220-2-IVTRODLCTION 3 2 ana the constraint ][ $ =1 General multi-pseudoparticle a=l a solutions have been founa for this case in Ref (7) by Belavm and Polyakov Introducing the angle parametrization for the unit vector * and defining D.STR.BUT.
Accomplishments are reported in the areas of string theory, nonperturbative analyses in quantum f... more Accomplishments are reported in the areas of string theory, nonperturbative analyses in quantum field theories, flavor gauge theory and grand unification theories, physics at the very early universe and quantum field theory, and critical phenomena in quantum field theory. (LEW)
The Journal of high energy physics/The journal of high energy physics, May 24, 2024
We construct a model of Pauli spin operators with all-to-all 4-local interactions by replacing Ma... more We construct a model of Pauli spin operators with all-to-all 4-local interactions by replacing Majorana fermions in the SYK model with spin operators. Equivalently, we replace fermions with hard-core bosons. We study this model numerically and compare the properties with those of the SYK model. We observe a striking quantitative coincidence between the spin model and the SYK model, which suggests that this spin model is strongly chaotic and, perhaps, can play some role in holography. We also discuss the path-integral approach with multi-local fields and the possibility of quantum simulations. This model may be an interesting target for quantum simulations because Pauli spins are easier to implement than fermions on qubit-based quantum devices.
We explore the question of finiteness of the entanglement entropy in gravitational theories whose... more We explore the question of finiteness of the entanglement entropy in gravitational theories whose emergent space is the target space of a holographic dual. In the well studied duality of two-dimensional non-critical string theory and c = 1 matrix model, this question has been studied earlier using fermionic many-body theory in the space of eigenvalues. The entanglement entropy of a subregion of the eigenvalue space, which is the target space entanglement in the matrix model, is finite, with the scale being provided by the local Fermi momentum. The Fermi momentum is, however, a position-dependent string coupling, as is clear in the collective field theory formulation. This suggests that the finiteness is a non-perturbative effect. We provide evidence for this expectation by an explicit calculation in the collective field theory of matrix quantum mechanics with vanishing potential. The leading term in the cumulant expansion of the entanglement entropy is calculated using exact eigenstates and eigenvalues of the collective Hamiltonian, yielding a finite result, in precise agreement with the fermion answer. Treating the theory perturbatively, we show that each term in the perturbation expansion is UV divergent. However the series can be resummed, yielding the exact finite result. Our results indicate that the finiteness of the entanglement entropy for higher dimensional string theories is non-perturbative as well, with the scale provided by the Newton constant. Dedicated to the memory of Ivan Andrić.
We extend the operator construction given by us earlier (for bosonic strings) to the Neveu-Schwar... more We extend the operator construction given by us earlier (for bosonic strings) to the Neveu-Schwarz-Ramond (NSR) superstrings. Witten's approach to interactions is followed. A construction of the interaction vertex for NS-NS-NS and NS-R-R string-states is given. The associated ghost interactions and the integration operator are also constructed explicitly. The field theory is formulated not only in the "bosonized" representation but also in the fundamental ghost representation. This allows a systematic expansion in terms of local fields.
We discuss the large N expansion in backgrounds of extended states with focus on implementation o... more We discuss the large N expansion in backgrounds of extended states with focus on implementation of Goldstone symmetries and the construction of the associated Hilbert space. The formulation is given in the general framework of collective field theory. Case of translational symmetry is described first, as the basic example. The large N thermofield represents the main topics, with the emergent dynamics of Left-Right bulk fields and collective symmetry coordinates. These give the basis for a 1/N expansion. Dedicated to the memory of Jean-Loup Gervais.
Springer proceedings in mathematics & statistics, 2018
In this article, starting from a review of basic aspects of the Sachdev-Ye-Kitaev (SYK) model in ... more In this article, starting from a review of basic aspects of the Sachdev-Ye-Kitaev (SYK) model in the large N limit, we discuss at non-linear-level the deduction of the zero mode effective Schwarzian action, featuring emergent finite reparametrization symmetry. We then discuss the question of identifying the bulk space-time of the SYK model. We explain the need for non-local (Radon-type) transformations on external legs of n-point Green’s functions, leading to a dual theory with Euclidean AdS signature with additional leg-factors. We show that the SYK spectrum and the bi-local propagator can be obtained from a Horava-Witten type compactification of a three dimensional model.
Progress in understanding and solving a large class of two-dimensional nonlinear quantum field th... more Progress in understanding and solving a large class of two-dimensional nonlinear quantum field theories is reviewed. The discovery and development of the inverse scattering method for solving partial differential equations, and development of new perturbative methods are discussed. The generalized Bethe-ansatz method and its application to exactly diagonalize a fermionic problem are covered. 52 references. (GHT)
The main emphasis in the theoretical program has been in the area of string theory; also investig... more The main emphasis in the theoretical program has been in the area of string theory; also investigated were confinement and other aspects of QCD, electroweak symmetry breaking, and electroweak baryogenesis. The research program in computational physics concentrated on the development of the source Galerkin method of numerical quantum field theory. One portion of the experimental program dealt with interactions of leptons and hadrons from accelerator and strophysics sources. A description of the Large Volume Detector at Gran Sasso and its use as a stellar collapse monitor is given, along with an account of research and development on resistive plate counters. The rest of the experimental program concerns hadron collider and neutrino physics, with major emphasis on the D0 experiment at the Tevatron. The commissioning of the D0 detector and its operation are described, along with D0 analysis. Also reported is a novel cryogenic technique utilizing superfluid helium for neutrino calorimetry.
We discuss point canonical transformations using the path integral quantization procedure. First,... more We discuss point canonical transformations using the path integral quantization procedure. First, employing the Feynman diagram technique we demonstrate how a formal treatment of point transformations leads to erroneous results. Then we present the correct treatment of this problem using a more precise definition of path integrals. We show how this more careful treatment leads to additional potential terms in the action as compared to the formal treatment. We also demonstrate the equivalence of our results with the corresponding operator method discussion. Furthermore, we investigate the consequences of these results on the path integral collective coordinate method. Giving the improved treatment on the one-soliton sector example we establish the path integral collective coordinate method of the same level of rigor as the parallel operator approaches.
We review two approaches to string dynamics: the renormalization group method and the string fiel... more We review two approaches to string dynamics: the renormalization group method and the string field theory formalism. The emphasis is on the relationship between these two seemingly different methods. The basic line of thought is that a renormalization group flow of a most general background coupled σ-model should lead to the equations of string field theory. Recent progress on this is summarized and a critical review of the results is given. Some new ideas concerning most general couplings are described.
We present an investigation of quantum fluctuations about pseudoparticle solutions in the two-dim... more We present an investigation of quantum fluctuations about pseudoparticle solutions in the two-dimensional a-model First, for the one pseudoparticle case, we solve the small oscillation problem and compute the first quantum correction to the classical result. In the two-pseudoparticle case, we transform the small oscillation problem into an ordinary Schrbdmger equation with an interaction depending on distance between the pseudo particles. We are then able to sclve the limiting cases of zero and infinite separations-NOTICE-This report was prepared as an account of work sponsored by the United States Government Neither the United States nor the United States Energy Research and Development Administration, nor any of their employees, nor any of their contractors subcontractors, or their employees makes any warranty express or implied, or assumes any legal liability or responsibility Tor the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights Research sponsored by_ the Energy Research and Development Administration, Grant No E(ll-l)-2220-2-IVTRODLCTION 3 2 ana the constraint ][ $ =1 General multi-pseudoparticle a=l a solutions have been founa for this case in Ref (7) by Belavm and Polyakov Introducing the angle parametrization for the unit vector * and defining D.STR.BUT.
Accomplishments are reported in the areas of string theory, nonperturbative analyses in quantum f... more Accomplishments are reported in the areas of string theory, nonperturbative analyses in quantum field theories, flavor gauge theory and grand unification theories, physics at the very early universe and quantum field theory, and critical phenomena in quantum field theory. (LEW)
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Papers by Antal Jevicki