- Armenia
Ruben Mkrtchyan
Yerevan Physics Institute, Theory, Department Member
Research Interests:
The algebra of volume-preserving vector fields is considered. The potentials for that fields are introduced, and induced algebra of potentials is considered. It is shown, that this algebra fails to satisfy the Jacoby identity. Analogy... more
The algebra of volume-preserving vector fields is considered. The potentials for that fields are introduced, and induced algebra of potentials is considered. It is shown, that this algebra fails to satisfy the Jacoby identity. Analogy with hamiltonian mechanics is developed, as well as 3-cocycle interpretation of corresponding expressions.
Research Interests:
We consider d=10, N=1 supersymmetry algebra with maximal number of tensor charges Z and introduce a class of orbits of Z, invariant w.r.t. the T8 subgroup of massless particles' little group T8⋉SO(8). For that class of orbits we classify... more
We consider d=10, N=1 supersymmetry algebra with maximal number of tensor charges Z and introduce a class of orbits of Z, invariant w.r.t. the T8 subgroup of massless particles' little group T8⋉SO(8). For that class of orbits we classify all possible orbits and little groups, which appear to be semidirect products T8⋉SO(k1)×ctdot×SO(kn), with k1+ctdot+kn=8, where compact factor is embedded into SO(8) by triality map. We define actions of little groups on supercharge Q and construct corresponding supermultiplets. In some particular cases we show the existence of supermultiplets with both Fermi and Bose sectors consisting of the same representations of tensorial Poincaré. In addition, complete classification of supermultiplets (not restricted to T8-invariant orbits) with rank-2 matrix of supersymmetry charges anticommutator, is given.
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We present the explicit formulas relating Hopf maps with Wigner's little groups. They, particularly, explain simple action of group on a fiber for the first and second Hopf fibrations, and present most simplified form for the third one.... more
We present the explicit formulas relating Hopf maps with Wigner's little groups. They, particularly, explain simple action of group on a fiber for the first and second Hopf fibrations, and present most simplified form for the third one. Corresponding invariant Lagrangians are presented, and their possible reductions are discussed.
Research Interests:
The little groups (i.e. the subgroups of Lorentz group, leaving invariant given configurations of tensorial charges) of unitary irreps of superstring/M-theory superalgebras are considered. It is noted, that in the case of $(n-1)/n$... more
The little groups (i.e. the subgroups of Lorentz group, leaving invariant given configurations of tensorial charges) of unitary irreps of superstring/M-theory superalgebras are considered. It is noted, that in the case of $(n-1)/n$ (maximal supersymmetric) BPS configuration in any dimensions the non-zero supercharge is neutral w.r.t. the algebra of little group, which means that all members of supermultiplet are in the same representation of that algebra and hence of (generalized with tensorial charges) Poincare algebra. This situation is similar to two-dimensional case and shows that usual spin-statistics connection statement is insufficient in the presence of branes, because different little groups can appear. We discuss the rules for definition of statistics for representations of generalized Poincare, and note that a geometric quantization method seems to be most relevant for that purpose.
Research Interests:
The simplest W-type algebra is considered, which includes spin-3/2 and 1 currents, with the aim of finding all its realizations in the free fermion theory through the currents of the type γi1…i2s ψi1 … ψi2s. The solution of this problem... more
The simplest W-type algebra is considered, which includes spin-3/2 and 1 currents, with the aim of finding all its realizations in the free fermion theory through the currents of the type γi1…i2s ψi1 … ψi2s. The solution of this problem appears to be related to some problem in the theory of Lie algebras, and we give a classification of the solutions for γ tensors, which turn out to be connected with structure constants of Lie algebras. This is in parallel with previously known similar bosonic construction, connected with symmetric counterpart of the Lie algebras — the Jordan algebras.
Research Interests:
We consider a few topics in E11 approach to superstrings/M-theory: even subgroups (Z2 orbifolds) of En, n = 11, 10, 9 and their connection to Kac-Moody algebras, particularly to EE11 subgroup of E11; possible form of supersymmetry... more
We consider a few topics in E11 approach to superstrings/M-theory: even subgroups (Z2 orbifolds) of En, n = 11, 10, 9 and their connection to Kac-Moody algebras, particularly to EE11 subgroup of E11; possible form of supersymmetry relation in E11; decomposition of first fundamental representation l1 w.r.t. the SO(10, 10) and its square-root at first few levels; particle orbit of l1 ⋉ E11. Possible relevance of coadjoint orbits method is noticed, based on a self-duality form of equations of motion in E11.
Research Interests:
The geometrical action for the algebra of area-preserving transformations of two-dimensional boundaryless manifolds (particularly for the torus) is constructed.
Little groups for preon branes (i.e. configurations of branes with maximal (n-1)/n fraction of survived supersymmetry) for dimensions d=2,3,…,11 are calculated for all massless, and partially for massive orbits. For massless orbits little... more
Little groups for preon branes (i.e. configurations of branes with maximal (n-1)/n fraction of survived supersymmetry) for dimensions d=2,3,…,11 are calculated for all massless, and partially for massive orbits. For massless orbits little groups are semidirect product of d-2 translational group Td-2 on a subgroup of (SO(d-2) × R-invariance) group. E.g. at d=9 the subgroup is exceptional G2 group. It is also argued, that 11D Majorana spinor invariants, which distinguish orbits, are actually invariant under d=2+10 Lorentz group. Possible applications of these results include construction of field theories in generalized spacetimes with brane charges coordinates, different problems of group's representations decompositions, spin-statistics issues.
Research Interests:
The Lagrangian of the minimal six-dimensional anomalous N=2 and N=4b supergravities are constructed which have all symmetries of these theories, in particular, explicit Lorentz-invariance and supersymmetry. They also have an additional... more
The Lagrangian of the minimal six-dimensional anomalous N=2 and N=4b supergravities are constructed which have all symmetries of these theories, in particular, explicit Lorentz-invariance and supersymmetry. They also have an additional local alpha -symmetry acting nontrivially only off the mass shell. Owing to this symmetry, the commutator of two supersymmetry transformations is closed on all boson fields without equations of motion. Other symmetry commutators of the theory are also calculated (alpha -symmetry and supersymmetry). The obtained Lagrangians are basic for the construction of those for six-dimensional chiral nonanomalous supergravities.
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Research Interests:
A contour equation for generalization of the Wilson Loop to the supersymmetric gauge theory is derived.
Research Interests:
In the study of conjecture on M-theory as a non-linear realization $E_{11}/K_{11}$ we present arguments for the following: 1)roots of $K_{11}$ coincide with the roots of Kac-Moody algebra $EE_{11}$ with Dynkin diagram given in the paper,... more
In the study of conjecture on M-theory as a non-linear realization $E_{11}/K_{11}$ we present arguments for the following: 1)roots of $K_{11}$ coincide with the roots of Kac-Moody algebra $EE_{11}$ with Dynkin diagram given in the paper, 2)one of the fundamental weights of $EE_{11}$ coincides with $l_1$ weight of $E_{11}$, known to contain 11d supergravity brane charges. The statement 1) is extended on $E_{10}$ and $E_9$ algebras.
ABSTRACT We provide a closed formula for the volume of a simple compact Lie group in terms of the universal Vogel parameters. For the unitary groups SU_n this reduces to the integral representation of the classical Barnes G-function.
The algebra of volume-preserving vector fields is considered. The potentials for that fields are introduced, and induced algebra of potentials is considered. It is shown, that this algebra fails to satisfy the Jacoby identity. Analogy... more
The algebra of volume-preserving vector fields is considered. The potentials for that fields are introduced, and induced algebra of potentials is considered. It is shown, that this algebra fails to satisfy the Jacoby identity. Analogy with hamiltonian mechanics is developed, as well as 3-cocycle interpretation of corresponding expressions.
Research Interests:
The little groups (i.e. the subgroups of Lorentz group, leaving invariant given configurations of tensorial charges) of unitary irreps of superstring/M-theory superalgebras are considered. It is noted, that in the case of $(n-1)/n$... more
The little groups (i.e. the subgroups of Lorentz group, leaving invariant given configurations of tensorial charges) of unitary irreps of superstring/M-theory superalgebras are considered. It is noted, that in the case of $(n-1)/n$ (maximal supersymmetric) BPS configuration in any dimensions the non-zero supercharge is neutral w.r.t. the algebra of little group, which means that all members of supermultiplet are in
Research Interests:
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ABSTRACT The geometrical action for the algebra of area-preserving transformations of two-dimensional boundaryless manifolds (particularly for the torus) is constructed.
Research Interests:
Research Interests:
Research Interests:
The simplest W-type algebra is considered, which includes spin-3/2 and 1 currents, with the aim of finding all its realizations in the free fermion theory through the currents of the type gammai1...i2s psii1 ... psii2s. The solution of... more
The simplest W-type algebra is considered, which includes spin-3/2 and 1 currents, with the aim of finding all its realizations in the free fermion theory through the currents of the type gammai1...i2s psii1 ... psii2s. The solution of this problem appears to be related to some problem in the theory of Lie algebras, and we give a classification of the solutions for gamma tensors, which turn out to be connected with structure constants of Lie algebras. This is in parallel with previously known similar bosonic construction, connected with symmetric counterpart of the Lie algebras --- the Jordan algebras.
Research Interests:
Research Interests:
Research Interests:
ABSTRACT In this paper some properties of the previously proposed lattice version of the Abelian Chern-Simons gauge theory are studied. The lattice analog of BF systems is constructed, and the properties of both theories are found to be... more
ABSTRACT In this paper some properties of the previously proposed lattice version of the Abelian Chern-Simons gauge theory are studied. The lattice analog of BF systems is constructed, and the properties of both theories are found to be in close correspondence with those of the continuous theory. The correspondence with two-dimensional lattice statistical systems is established and the lattice origin of the framing of Wilson loops is shown.
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ABSTRACT The supersymmetry and α-symmetry of the complete Lagrangian of pure d = 6 N = 4b supergravity are proved.
We show that partition function of Chern-Simons theory on three-sphere with classical and exceptional groups (actually on the whole corresponding lines in Vogel's plane) can be represented as ratio of respectively triple and double sine... more
We show that partition function of Chern-Simons theory on three-sphere with classical and exceptional groups (actually on the whole corresponding lines in Vogel's plane) can be represented as ratio of respectively triple and double sine functions (last function is essentially a modular quantum dilogarithm). The product representation of sine functions gives Gopakumar-Vafa structure form of partition function, which in turn gives a corresponding integer invariants of manifold after geometrical transition. In this way we suggest to extend gauge/string duality to exceptional groups, although one still have to resolve few problems. In both classical and exceptional cases an additional terms, non-perturbative w.r.t. the string coupling constant, appear. The full universal partition function of Chern-Simons theory on three-sphere is shown to be the ratio of quadruple sine functions. We also briefly discuss the matrix model for exceptional line.
Research Interests:
We show that both perturbative and non-perturbative parts of universal partition functions of Chern-Simons theory on 3d sphere are ratios of four over four Barnes' quadruple gamma functions with arguments given by linear combinations of... more
We show that both perturbative and non-perturbative parts of universal partition functions of Chern-Simons theory on 3d sphere are ratios of four over four Barnes' quadruple gamma functions with arguments given by linear combinations of universal parameters. Since nonperturbative part of partition function is essentially a universal compact simple Lie group's volume, latter appears to be expressed through quadruple Barnes' functions, also. For SU(N) values of parameters recurrent relations on Barnes' functions give the proof of level-rank duality of complete partition function, thus extending that duality on non-integer level and rank. We note that integral representation of universal partition function is defined on few disjoint regions in parameters' space, corresponding to different signs of real parts of parameters, and introduce a framework for discussion of analytic continuation of partition functions(s) from these regions. Although initial integral representation is symmetric under all permutations of parameters (which corresponds particularly to $N \rightarrow -N$ duality of gauge theories with classical groups), analytic continuations are not symmetric under transposition of parameters with different signs of their real parts. For the particular case of SU(N) Chern-Simons this asymmetry appears to be the Kinkelin's functional equation (reflection relation) for Barnes' G-function.
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Closed simple integral representation through Vogel's universal parameters is found both for perturbative and nonperturbative (which is inverse invariant group volume) parts of free energy of Chern-Simons theory on $S^3$. This proves the... more
Closed simple integral representation through Vogel's universal parameters is found both for perturbative and nonperturbative (which is inverse invariant group volume) parts of free energy of Chern-Simons theory on $S^3$. This proves the universality of that partition function. For classical groups it manifestly satisfy $N \rightarrow - N$ duality, in apparent contradiction with previously used ones. For $SU(N)$ we show that asymptotic of nonperturbative part of our partition function coincides with that of Barnes G-function, recover Chern-Simons/topological string duality in genus expansion and resolve abovementioned contradiction. We discuss few possible directions of development of these results: derivation of representation of free energy through Gopakumar-Vafa invariants, possible appearance of non-perturbative additional terms, $1/N$ expansion for exceptional groups, duality between string coupling constant and K\"ahler parameters, etc.
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We show that the perturbative part of the partition function in the Chern-Simons theory on a 3-sphere as well as the central charge and expectation value of the unknotted Wilson loop in the adjoint representation can be expressed in terms... more
We show that the perturbative part of the partition function in the Chern-Simons theory on a 3-sphere as well as the central charge and expectation value of the unknotted Wilson loop in the adjoint representation can be expressed in terms of the universal Vogel's parameters $\alpha, \beta, \gamma.$ The derivation is based on certain generalisations of the Freudenthal-de Vries strange formula.
Research Interests:
For two different natural definitions of Casimir operators for simple Lie algebras we show that their eigenvalues in the adjoint representation can be expressed polynomially in the universal Vogel's parameters $\alpha, \beta, \gamma$ and... more
For two different natural definitions of Casimir operators for simple Lie algebras we show that their eigenvalues in the adjoint representation can be expressed polynomially in the universal Vogel's parameters $\alpha, \beta, \gamma$ and give explicit formulae for the generating functions of these eigenvalues.
Research Interests:
The 12d supersymmetry algebra is considered, and classification of BPS states for some canonical form of second-rank central charge is given. It is shown, that possible fractions of survived supersymmetry can be 1/16, 1/8, 3/16, 1/4, 5/16... more
The 12d supersymmetry algebra is considered, and classification of BPS states for some canonical form of second-rank central charge is given. It is shown, that possible fractions of survived supersymmetry can be 1/16, 1/8, 3/16, 1/4, 5/16 and 1/2, the values 3/8, 7/16 cannot be achieved in this way. The consideration of a special case of non-zero sixth-rank tensor charge also is included.
, is extended to include interaction. For SO(2,2) gravity in a tensorial space-time, with space-time symmetry consisting of Lorentz generators and "translations", represented by second-rank antisymmetric tensor, the cubic interaction... more
, is extended to include interaction. For SO(2,2) gravity in a tensorial space-time, with space-time symmetry consisting of Lorentz generators and "translations", represented by second-rank antisymmetric tensor, the cubic interaction terms are constructed by requirement of maintaining the gauge invariance property of theory. This interaction is essentially unique.
Free field equations, with various spins, for space-time algebras with second-rank tensor (instead of usual vector) momentum are constructed. Similar algebras are appearing in superstring/M theories. The most attention is payed to the... more
Free field equations, with various spins, for space-time algebras with second-rank tensor (instead of usual vector) momentum are constructed. Similar algebras are appearing in superstring/M theories. The most attention is payed to the gauge invariance properties, particularly the spin two equations with gauge invariance are constructed for dimensions 2+2 and 2+4 and connection to Einstein equation and diffeomorphism invariance is established.
The geometric action on a certain orbit of the group of the area-preserving diffeomorphisms is considered, and it is shown, that it coincides with a special reduction of the three-dimensional Chern-Simons theory, under which group and... more
The geometric action on a certain orbit of the group of the area-preserving diffeomorphisms is considered, and it is shown, that it coincides with a special reduction of the three-dimensional Chern-Simons theory, under which group and space coordinates are identified.