Alternative method of calculating the eigenvalues of the transfer matrix of the τ<Subscript>2</Subscript> model for <Emphasis Type="Italic">N</Emphasis> = 2

It has been shown that the τ₂ (Baxter-Bazhanov-Stroganov) model for N = 2 with arbitrary parameters is a particular case of the generalized Ising model. The model satisfies the free-fermion condition, which enables one to solve it by the method of the auxiliary Grassmann field. Explicit expressions have been derived for the partition function on a finite-size lattice and eigenvalues of the transfer matrix. In this approach, in contrast to the functional relation method, there is no problem with the multiplicities of the eigenvalues of transfer matrix.     

Spontaneous supersymmetry breaking in large-N matrix models with slowly varying potential

We construct a class of matrix models, where supersymmetry (SUSY) is spontaneously broken at the matrix size N infinite. The models are obtained by dimensional reduction of matrix-valued SUSY quantum mechanics. The potential of the models is slowly varying, and the large-N limit is taken with the slowly varying limit.     

Stochastic and parastochastic aspects of supersymmetric functional measures: A new non-perturbative approach to supersymmetry

We study the properties of supersymmetric models having a local Nicolai mapping. In these cases the Nicolai mapping can be interpreted as a stochastic differential equation, and hence we can use all the standard stochastic techniques to extract physical information from the theory. The corresponding Langevin equation does not describe, in general, a system approaching (asymptotically) a thermal equilibrium. We construct explicitly and nonperturbatively the Nicolai mapping for a large class of two dimensional models. In particular, this is the first non-perturbative proof of the existence of the mapping. The properties of the mapping agree with the expectations from general arguments. We show how the Nicolai mapping can be used to eliminate completely the fermions from the perturbative expansion, leaving a simpler set of diagrammatric rules involving only scalars. Finally, we argue that the present approach may be very powerful for studying finiteness properties of extended supersymmetric theories.     

Self duality in super Yang-Mills theories

The self dual condition in superspace is analysed forN=1,2,4 super Yang-Mills theories. A complete solution of all the constraints in terms of a light cone superfieldJ is presented, where the only equation thatJ satisfies is a SUSY generalization of the Yang equation. By reduction of that equation we obtain various two dimensional SUSY models. We introduce the associated linear problem in terms ofJ, whose integrability condition gives us back the super Yang equation and allows us to obtain the Kac-Moody algebra structure of the theory.     

Coherent State Path Integral for the Harmonic Oscillator and a Spin Particle in a Constant Magnetic field

Definition and formulas for harmonic oscillator coherent states and spin coherent states are reviewed in detail. The path integral formalism and its relation with the partition function of a system are also reviewed. The harmonic oscillator coherent state path integral is evaluated exactly at the discrete level and then used to find its continuum limit using various regularizations. The computation of the path integral for a particle of spin s put in a constant magnetic field is carried out using harmonic oscillator coherent states and spin coherent states, with a careful analysis of infinitesimal terms (in 1/N where N is the number of time slices) appearing in the Lagrangian. A mapping of the spin system into a CP¹ model is shown explicitly. The theory of a spinless particle in the field of a magnetic monopole and its relation with the spin system are explained. The equivalence of these two models is established up to infinitesimal order by the introduction of an external field correction. This gives a new representation of a coherent state path integral in terms of a more familiar Feynman path integral.     

Bistability of radiation force on N-atom system

We consider a system with N two-level atoms in a cavity, interacting with an external radiation field. Using Ehrenfest's theorem the radiation force on the N-atom system is studied as a function of the external radiation field. In a certain parameter region we are able to show that the radiation force can be bistable     

Lattice supersymmetry and the nicolai mapping

We propose the use of the Nicolai mapping as a guiding principle for formulating supersymmetric theories on a discrete space-time lattice, on which the supersymmetry algebra is not well-defined. We present a discretized form of the N = 2 Wess-Zumino model in 1+1 dimensions. This model is also examined in the hamiltonian (continuous time) formalism on a spatial lattice, and is found to allow consistent discretization only for those subalgebras which admit an internal O(2) symmetry.     

Stochastic processes in lattice (extended) supersymmetry

We show that ungauged N = 2 supersymetric models can be put on the (hamiltonian) lattice in such a way as to preserve a subalgebra of supersymmetry large enough to ensure the existence of the Nicolai mapping. The models can be interpreted as stochastic systems described by Langevin equations. We describe both Wilson and Susskind versions of the model.In two dimensions everything seems fine, but in 4D, one expects, on general grounds, that the continuum limit will be either trivial or non-Lorentz invariant.     

Constraints on light particles from kaon decays

It is shown how auxiliary field tadpoles may be used to calculate the effective potential in SUSY gauge theories. SUSY QED and SUSY QCD are given as examples.     

Equivalent lagrangians in large N field theories

The auxiliary field method is generalized to any O (N)-invariant theory with non-polynomial interactions. In non-supersymmetric theories, two lagrangians with and without an auxiliary field are shown to be equivalent to the leading order of the 1/N expansion. In supersymmetric theories, these two lagrangians are equivalent to all orders of the 1/N expansion. The lagrangian with an auxiliary field is solvable in the 1/N expansion.     

F-theorem, duality and SUSY breaking in one-adjoint Chern-Simons-Matter theories

We extend previous work on N=2 Chern-Simons theories coupled to a single adjoint chiral superfield using localization techniques and the F-maximization principle. We provide tests of a series of proposed 3D Seiberg dualities and a new class of tests of the conjectured F-theorem. In addition, a proposal is made for a modification of the F-maximization principle that takes into account the effects of decoupling fields. Finally, we formulate and provide evidence for a new general non-perturbative constraint on spontaneous supersymmetry breaking in three dimensions based on Q-deformed S³ partition functions. An explicit illustration based on the known analytic solution of the Chern-Simons matrix model is presented.     

The large N expansion as a local perturbation theory

The partition function of an O(N)-invariant vector anharmonic oscillator is generated by a set of Hamiltonians describing one-component oscillators in double-well potentials at negative coupling constant. The large N expansion appears as a conventional perturbation theory for auxiliary scalar Hamiltonians. An extension of the approach to rotationally invariant vector field theories is considered in the framework of the bilocal formalism.     

Two-dimensional supersymmetry: From SUSY quantum mechanics to integrable classical models

Two known two-dimensional SUSY quantum mechanical constructions—the direct generalization of SUSY with first-order supercharges and higher-order SUSY with second-order supercharges—are combined for a class of 2-dim quantum models, which are not amenable to separation of variables. The appropriate classical limit of quantum systems allows us to construct SUSY-extensions of original classical scalar Hamiltonians. Special emphasis is placed on the symmetry properties of the models thus obtained—the explicit expressions of quantum symmetry operators and of classical integrals of motion are given for all (scalar and matrix) components of SUSY-extensions. Using Grassmanian variables, the symmetry operators and classical integrals of motion are written in a unique form for the whole Superhamiltonian. The links of the approach to the classical Hamilton-Jacobi method for related “flipped” potentials are established.     

Note on the Harmonic Approximation in the Treatment of Entanglement: N Cold Trapped Ions

We study a one-dimensional system composed of N charged bosons confined in an external harmonic potential. In the limit of a strong interaction between the particles, we apply the harmonic approximation and derive an integral representation for the purity of the one-particle reduced density matrix, enabling an easy determination of the asymptotic entanglement. Results for the dependence of the asymptotic linear entropy on N are provided and discussed in detail for the first time.     

Matrix Representation of the Stationary Measure for the Multispecies TASEP

In this work we construct the stationary measure of the N species totally asymmetric simple exclusion process in a matrix product formulation. We make the connection between the matrix product formulation and the queueing theory picture of Ferrari and Martin. In particular, in the standard representation, the matrices act on the space of queue lengths. For N>2 the matrices in fact become tensor products of elements of quadratic algebras. This enables us to give a purely algebraic proof of the stationary measure which we present for N=3.     

Instanton effects in N = 2 supersymmetric quantum mechanics

Supersymmetric quantum mechanics with several bosonic and fermionic dynamic variables is considered. Two different N = 2 supersymmetric models involving instantons are discussed in detail. Instantons fail to break supersymmetry in one of the models considered. The vacuum state is degenerate in this model which generally results in spontaneous breaking of internal left-right symmetry. In another model supersymmetry is destroyed dynamically due to special complex instanton solutions. Possible implications for SUSY field theories are discussed.     

Instanton effects in supersymmetric gauge theories

We investigate how in supersymmetric gauge theories non-perturbative effects are able to generate non-trivial vacuum properties otherwise forbidden by perturbative non-renormalization theorems. This conclusion can be reliably drawn since the constancy of certain Green functions — due to supersymmetry (SUSY) — allows one to connect vacuum-dominated large distances with short-distance behaviour which is reliably computed by instanton methods. In all the cases we discuss (without matter, with massive or massless matter in real representations and, finally, with matter in complex representations) instanton calculations imply the occurrence of a variety of condensates. For the pure SUSY gauge theory, a gluino condensate induces the spontaneous breaking of Z_2N. For massive super-quantum chromodynamics (SQCD) we find a peculiar mass dependence of matter condensates whose origin is traced to mass singularities of non-zero mode instanton contributions. These contributions force the massless limit of SQCD to differ from the strictly massless case, in which the spontaneous breaking of chiral symmetries is induced. Inconsistency with an anomaly equation forces either infinite matter condensates or spontaneous SUSY breaking in the massless cases. For non-constant Green functions, instantons are shown to provide new calculable short-distance singularities of an obvious non-perturbative nature.