Searcharxiv⌕ Search

arXiv subjects

A. V. Smilga

Publications and source records attributed to A. V. Smilga.

At least 37 records · Page 2Linked to original sources
arXiv2014

Multidimensional Dirac strings and the Witten index of SYMCS theories with groups of higher rank

We discuss generalized Dirac strings associated with a given Lie group. They live in r-dimensional complex space (r being the rank of the group). Such strings show up in the effective Born-Oppenheimer Hamiltonian for 3d supersymmetric Yang-Mills-Chern-Simons theories, brought up by the gluon loops. We calculate accurately the number of the vacuum states in the effective Hamiltonian associated with these strings. We also show that these states are irrelevant for the final SYMCS vacuum counting. The Witten index of SYMCS theories depends thus only on the strings generated by fermion loops and carrying fractional generalized fluxes.

hep-th↗
arXiv2014

Supersymmetric field theory with benign ghosts

We construct a supersymmetric (1+1)-dimensional field theory involving extra derivatives and associated ghosts: the spectrum of the Hamiltonian is not bounded from below, neither from above. In spite of that, there is neither classical, nor quantum collapse and unitarity is preserved.

hep-th↗
arXiv2013

Taming the zoo of supersymmetric quantum mechanical models

We show that in many cases nontrivial and complicated supersymmetric quantum mechanical (SQM) models can be obtained from the simple model describing free dynamics in flat complex space by two operations: (i) Hamiltonian reduction and (ii) similarity transformation of the complex supercharges. We conjecture that it is true for any SQM model.

math-ph↗
arXiv2013

Supercharges in the HKT Supersymmetric Sigma Models

We construct explicitly classical and quantum supercharges satisfying the standard N = 4 supersymmetry algebra in the supersymmetric sigma models describing the motion over HKT (hyper-Kaehler with torsion) manifolds. One member of the family of superalgebras thus obtained is equivalent to the superalgebra derived and formulated earlier in the purely mathematical framework.

math-ph↗
arXiv2012

Dirac Operator on Complex Manifolds and Supersymmetric Quantum Mechanics

We explore a new simple N=2 SQM model describing the motion over complex manifolds in external gauge fields. The nilpotent supercharge Q of the model can be interpreted as a (twisted) exterior holomorphic derivative, such that the model realizes the twisted Dolbeault complex. The sum Q + \bar Q can be interpreted as the Dirac operator: the standard Dirac operator if the manifold is Kähler and a certain "truncated" Dirac operator for a generic complex manifold. Focusing on the Kähler case, we give new simple physical proofs of the two mathematical facts: (i) the equivalence of the twisted Dirac and twisted Dolbeault complexes and (ii) the Atiyah-Singer theorem.

hep-th↗
arXiv2012

Real and complex supersymmetric d=1 sigma models with torsions

We derive and discuss, at both the classical and the quantum levels, generalized N = 2 supersymmetric quantum mechanical sigma models describing the motion over an arbitrary real or an arbitrary complex manifold with extra torsions. We analyze the relevant vacuum states to make explicit the fact that their number is not affected by adding the torsion terms.

hep-th↗
arXiv2012

Once more on the Witten index of 3d supersymmetric YM-CS theory

The problem of counting the vacuum states in the supersymmetric 3d Yang-Mills-Chern-Simons theory is reconsidered. We resolve the controversy between its original calculation by Witten at large volumes and the calculation based on the evaluation of the effective Lagrangian in the small volume limit. We show that the latter calculation suffers from uncertainties associated with the singularities in the moduli space of classical vacua where the Born-Oppenheimer approximation breaks down. We also show that these singularities can be accurately treated in the Hamiltonian Born-Oppenheimer method, where one has to match carefully the effective wave functions on the Abelian valley and the wave functions of reduced non-Abelian QM theory near the singularities. This gives the same result as original Witten's calculation.

hep-th↗
arXiv2012

Witten index in supersymmetric 3d theories revisited

We have performed a direct calculation of Witten index in N = 1,2,3 supersymmetric Yang-Mills Chern-Simons 3d theories. We do it in the framework of Born-Oppenheimer (BO) approach by putting the system into a small spatial box and studying the effective Hamiltonian depending on the zero field harmonics. At the tree level, our results coincide with the results of Witten, but there is a difference in the way the loop effects are implemented. In Witten's approach, one has only take into account the fermion loops, which bring about a negative shift of the (chosen positive at the tree level) Chern-Simons coupling k. As a result, Witten index vanishes and supersymmetry is broken at small k. In the effective BO Hamiltonian framework, fermion, gluon and ghost loops contribute on an equal footing. Fermion loop contribution to the effective Hamiltonian can be evaluated exactly, and their effect amounts to the negative shift k -> k - h/2 for N =1 and k -> k - h for N = 2,3 in the tree-level formulae for the index. In our approach, with rather natural assumptions on the structure of bosonic corrections, the shift k -> k + h brought about by the gluon loops also affects the index. Since the total shift of k is positive or zero, Witten index appears to be nonzero at nonzero k, and supersymmetry is not broken. We discuss possible reasons for such disagreement.

hep-th↗
arXiv2009

Energy losses in a hot plasma revisited

We present a mini-review of the problem of evaluating the energy loss of a ultrarelativistic charged particle crossing a thermally equilibrated high temperature e+e- or quark-gluon plasma.

hep-ph↗
arXiv2009

Exceptional points in quantum and classical dynamics

We notice that, when a quantum system involves exceptional points, i.e. the special values of parameters where the Hamiltonian loses its self-adjointness and acquires the Jordan block structure, the corresponding classical system also exhibits a singular behaviour associated with restructuring of classical trajectories. The system with the crypto-Hermitian Hamiltonian H = (p^2+z^2)/2 -igz^5 and hyper-ellictic classical dynamics is studied in details. Analogies with supersymmetric Yang-Mills dynamics are elucidated.

math-ph↗
arXiv2008

Comments on thermodynamics of supersymmetric matrix models

We present arguments that the structure of the spectrum of the supersymmetric matrix model with 16 real supercharges in the large N limit is rather nontrivial, involving besides the natural energy scale ~λ^{1/3} = (g^2 N)^{1/3} also a lower scale ~λ^{1/3}N^{-5/9}. This allows one to understand a nontrivial behaviour of the mean internal energy of the system, E proportional to T^{14/5}, predicted by AdS duality arguments.

hep-th↗
arXiv2008

Physics of crypto-Hermitian and/or cryptosupersymmetric field theories

We discuss non-Hermitian field theories where the spectrum of the Hamiltonian involves only real energies. We make three observations. (i) The theories obtained from supersymmetric theories by nonanticommutative deformations belong in many cases to this class. (ii) When the deformation parameter is small, the deformed theory enjoys the same supersymmetry algebra as the undeformed one. Half of the supersymmetries are manifest and the existence of another half can be deduced from the structure of the spectrum. (iii) Generically, the conventionally defined S--matrix is not unitary for such theories.

hep-th↗
arXiv2008

Crypto-Hermiticity of nonanticommutative theories

We note that, though nonanticommutative deformations of Minkowski supersymmetric theories do not respect the reality condition and seem to lead to non-Hermitian Hamiltonians H, the latter belong to the class of crypto-Hermitian (or quasi-Hermitian) Hamiltonians having attracted recently a considerable attention. They can be made manifestly Hermitian via the similarity transformation H -> e^R H e^{-R} with a properly chosen R. The deformed model enjoys the same supersymmetry algebra as the undeformed one though it is difficult in some cases to write explicit expressions for a half of supercharges. The deformed SQM models make perfect sense. It is not clear whether it is also the case for NAC Minkowski field theories -- the conventionally defined S--matrix is not unitary there.

hep-th↗
arXiv2007

Cryptogauge symmetry and cryptoghosts for crypto-Hermitian Hamiltonians

We discuss the Hamiltonian H = p^2/2 - (ix)^{2n+1} and the mixed Hamiltonian H = (p^2 + x^2)/2 - g(ix)^{2n+1}, which are crypto-Hermitian in a sense that, in spite of apparent complexity of the potential, a quantum spectral problem can be formulated such that the spectrum is real. We note first that the corresponding classical Hamiltonian system can be treated as a gauge system, with imaginary part of the Hamiltonian playing the role of the first class constraint. We observe then that, on the basis of this classical problem, several different nontrivial quantum problems can be formulated. We formulate and solve some such problems. We find in particular that the spectrum of the mixed Hamiltonian undergoes in certain cases rather amazing transformation when the coupling g is sent to zero. There is an infinite set of phase transitions in g when a couple of eigenstates of H coalesce and disappear from the spectrum. When quantization is done in the most natural way such that gauge constraints are imposed on quantum states, the spectrum should not be positive definite, but must involve the negative energy states (ghosts). We speculate that, in spite of the appearance of ghost states, unitarity might still be preserved.

quant-ph↗
arXiv2007

Cryptoreality of nonanticommutative Hamiltonians

We note that, though nonanticommutative (NAC) deformations of Minkowski supersymmetric theories do not respect the reality condition and seem to lead to non-Hermitian Hamiltonians H, the latter belong to the class of ``cryptoreal'' Hamiltonians considered recently by Bender and collaborators. They can be made manifestly Hermitian via the similarity transformation H -> exp{R} H exp{-R} with a properly chosen R. The deformed model enjoys the same supersymmetry algebra as the undeformed one, though being realized differently on the involved canonical variables. Besides quantum-mechanical models, we treat, along similar lines, some NAC deformed field models in 4D Minkowski space.

hep-th↗
arXiv2006

On dynamics of 5D superconformal theories

5D superconformal theories involve vacuum valleys characterized in the simplest case by the vacuum expectation value of a real scalar field. If it is nonzero, conformal invariance is spontaneously broken and the theory is not renormalizable. In the conformally invariant sector with zero scalar v.e.v., the theory is intrinsically nonperturbative. We study classical and quantum dynamics of this theory in the limit when field dependence of the spatial coordinates is disregarded. The classical trajectories ``fall'' on the singularity at the origin of scalar moduli space. The quantum spectrum involves ghost states with unbounded from below negative energies, but such states fail to form complete 16-plets as is dictated by the presence of four complex supercharges and should be rejected by that reason. Physical excited states come in supermultiplets and have all positive energies. We conjecture that the spectrum of the complete field theory hamiltonian is nontrivial and has a similar nontrivial ghost-free structure and also speculate that the ghosts in higher-derivative supersymmetric field theories are exterminated by a similar mechanism.

hep-th↗
arXiv2006

Description of Quantum Entanglement with Nilpotent Polynomials

We propose a general method for introducing extensive characteristics of quantum entanglement. The method relies on polynomials of nilpotent raising operators that create entangled states acting on a reference vacuum state. By introducing the notion of tanglemeter, the logarithm of the state vector represented in a special canonical form and expressed via polynomials of nilpotent variables, we show how this description provides a simple criterion for entanglement as well as a universal method for constructing the invariants characterizing entanglement. We compare the existing measures and classes of entanglement with those emerging from our approach. We derive the equation of motion for the tanglemeter and, in representative examples of up to four-qubit systems, show how the known classes appear in a natural way within our framework. We extend our approach to qutrits and higher-dimensional systems, and make contact with the recently introduced idea of generalized entanglement. Possible future developments and applications of the method are discussed.

quant-ph↗