Stochastic quantization of supersymmetric field theory

The Parisi-Wu stochastic quantization method is applied to supersymmetric field theory. The Langevin equation, which reproduces the Green functions of euclidean field theory, is written in terms of superfields. Supersymmetric U(1) theory under gauge fixing and the large N reduction in chiral SU(N) theory are discussed. Regularization based on the stochastic method is studied also.     

Duality in Sp and SO gauge groups from M theory

We describe fivebrane configurations in M theory whose 4-d spacetime contains N = 1 supersymmetric Sp or SO gauge fields and fundamentals of these groups. We show how field-theory dualities for Sp and SO groups can be derived using these fivebrane configurations in M theory.     

Reflection matrices for integrable N = 1 supersymmetric theories

We study two-dimensional integrable N = 1 supersymmetric theories (without topological charges) in the presence of a boundary. We find a universal ratio between the reflection amplitudes for particles that are related by supersymmetry and we propose exact reflection matrices for the supersymmetric extensions of the multi-component Yang-Lee models and for the breather multiplets of the supersymmetric sine-Gordon theory. We point out the connection between our reflection matrices and the classical boundary actions for the supersymmetric sine-Gordon theory as constructed by Inami, Odake and Zhang [Phys. Lett. B 359 (1995) 118].     

On the integrable hierarchies associated with the N = 2 super Wn algebra

A new Lax operator is proposed from the viewpoint of constructing the integrable hierarchies related with the N = 2 super W_n algebra. It is shown that the Poisson algebra associated to the second Hamiltonian structure for the resulting hierarchy contains the N = 2 super Virasoro algebra as a proper subalgebra. The simplest cases are discussed in detail. In particular, it is proved that the supersymmetric two-boson hierarchy is one of the N = 2 supersymmetric KdV hierarchies. Also, a Lax operator is supplied for one of the N = 2 supersymmetric Boussinesq hierarchies.     

Exactly solvable diffusion models in the framework of the extended supersymmetric quantum mechanics

This work is aimed at demonstrating the possibility to construct new exactly-solvable stochastic systems by use of the extended supersymmetric quantum mechanics (N=4SUSY QM) formalism. A feature of the proposed approach consists in the fact that obtained new potentials, which enter the Langevin equation, and so probability densities have a parametric freedom. The latter allows one to change the form of potentials without changing the temporal behavior of the probability densities.     

Dynamical supersymmetry breaking and gauge anomalies

Some aspects of supersymmetric gauge theories and discussed. It is shown that dynamical supersymmetry breaking does not occur in supersymmetric QED in higher dimensions. The cancellation of both local (perturbative) and global (non-perturbative) gauge anomalies are also discussed in supersymmetric gauge theories. We argue that there is no dynamical supersymmetry breaking in higher dimensions in any supersymmetric gauge theories free of gauge anomalies. It is also shown that for supersymmetric gauge theories in higher dimensions with a compact connected simple gauge group, when the local anomaly-free condition is satisfied, there can be at most a possibleZ ₂ global gauge anomaly in extended supersymmetricSO(10) (or spin (10)) gauge theories inD=10 dimensions containing additional Weyl fermions in a spinor representation ofSO(10) (or spin (10)). In four dimensions with local anomaly-free condition satisfied, the only possible global gauge anomalies in supersymmetric gauge theories areZ ₂ global gauge anomalies for extended supersymmetricSP(2N) (N=rank) gauge theories containing additional Weyl fermions in a representation ofSP(2N) with an odd 2nd-order Dynkin index.     

The N = 2 Supersymmetric Unconstrained Matrix GNLS Hierarchies

The generalization of the N = 2 supersymmetric chiral matrix (k | n,m)-GNLS hierarchy (Lett. Math. Phys. 45 (1998) 63, solv-int/9711009) to the case when matrix entries are bosonic and fermionic unconstrained N = 2 superfields is proposed. This is done by exhibiting the corresponding matrix Lax-pair representation in terms of N = 2 unconstrained superfields. It is demonstrated that when matrix entries are chiral and antichiral N = 2 superfields, it reproduces the N = 2 chiral matrix (k | n,m)-GNLS hierarchy, while in the scalar case, k = 1, it is equivalent to the N = 2 supersymmetric multicomponent hierarchy (J. Phys. A 29 (1996) 1281, hep-th/9510185). The simplest example—the N = 2 unconstrained (1 | 1,0)-GNLS hierarchy—and its reduction to the N = 2 supersymmetric = 1 KdV hierarchy are discussed in more detail, and its rich symmetry structure is uncovered.     

Higher derivative regulation of supersymmetric theories

The rigid N = 1 supersymmetric theories are regulated using higher derivatives, supplemented with one-loop Pauli-Villars regulator fields. This scheme preserves supersymmetry as well as background and quantum gauge invariances.     

N = 2 supersymmetric Yang-Mills theory and its supercurrent

Using the off-shell two-component formulation of N = 2 supersymmetric Yang-Mills theory and the gauge covariantized supersymmetry transformations for the fields, the non-abelian supercurrent and anomaly multiplets are developed and the transformation rules for their components are obtained. The superfields in N = 2 superspace whose components are the non-abelian supercurrent and anomaly multiplets are written down.     

Odd Hamiltonian structure for supersymmetric Sawada-Kotera equation

We study the supersymmetric N=1 hierarchy connected with the Lax operator of the supersymmetric Sawada-Kotera equation. This operator produces the physical equations as well as the exotic equations with odd time. The odd Bi-Hamiltonian structure for the N=1 supersymmetric Sawada-Kotera equation is defined. The product of the symplectic and implectic Hamiltonian operator gives us the recursion operator. In that way we prove the integrability of the supersymmetric Sawada-Kotera equation in the sense that it has the Bi-Hamiltonian structure. The so-called “quadratic” Hamiltonian operator of even order generates the exotic equations while the “cubic” odd Hamiltonian operator generates the physical equations.     

On the functional integration measure of supersymmetric Yang-Mills theories

For the simplest N = 1 supersymmetric Yang-Mills theory, we construct a bosonic field transformation which linearizes the Yang-Mills action in each topological sector and whose jacobian equals the product of Fadeev-Popov and Matthews-Salam determinants up to cubic order at least. Some possible implications of this result for the maximally extended N = 4 theory are discussed.     

Semi-classical spectrum of the homogeneous sine-Gordon theories

The semi-classical spectrum of the homogeneous sine-Gordon theories associated with an arbitrary compact simple Lie group G is obtained and shown to be entirely given by solitons. These theories describe quantum integrable massive perturbations of Gepner's G-parafermions whose classical equations-of-motion are non-abelian affine Toda equations. One-soliton solutions are constructed by embeddings of the SU(2) complex sine-Gordon soliton in the regular SU(2) subgroups of G. The resulting spectrum exhibits both stable and unstable particles, which is a peculiar feature shared with the spectrum of monopoles and dyons in N = 2 and N = 4 supersymmetric gauge theories.     

Towards the construction of N = 2 supersymmetric integrable hierarchies

We formulate a conjecture for the three different Lax operators that describe the bosonic sectors of the three possible N = 2 supersymmetric integrable hierarchies with N = 2 super-W_n second Hamiltonian structure. We check this conjecture in the simplest cases, then we verify it in general in one of the three possible supersymmetric extensions. To this end we construct the N = 2 supersymmetric extensions of the Generalized Non-Linear Schrödinger hierarchy by exhibiting the corresponding super Lax operator. To find the correct Hamiltonians we are led to a new definition of super-residues for degenerate N = 2 supersymmetric pseudo-differential operators. We have found a new non-polynomials Miura-like realization for N = 2 superconformal algebra in terms of two bosonic chiral-anti-chiral free superfields.     

Solution of the entropy crisis of supersymmetric theories

Most supersymmetric models possess a decoupled particle with mass of order M_W which is copiously produced in the early universe and whose decays produce huge amounts of entropy. We show how this problem is avoided in theories in which the hidden sector contains several light fields.     

Background field formalism and construction of effective action for N = 2, d = 3 supersymmetric gauge theories

We review the background field method for three-dimensional Yang-Mills and Chern-Simons models in N = 2 superspace. Superfield proper time (heat kernel) techniques are developed and exact expressions of heat kernels for constant backgrounds are presented. The background field method and heat kernel techniques are applied for evaluating the low-energy effective actions in N = 2 supersymmetric Yang-Mills and Chern-Simons models as well as in N = 4 and N = 8 SYM theories.     

Supersymmetric gauge theories in quantum mechanics

A general construction for supersymmetric U(1) gauge invariant Hamiltonians in quantum mechanics is given. For a given number of fermionic and bosonic degrees of freedom it is shown that for four supercharges the interactions are determined uniquely, and coincide with the dimensionally reduced N = 1, d = 3 + 1 supersymmetric electrodynamics. With two supercharges one gets models which cannot be obtained through dimensional reduction. For two special choices of a parameter one recovers the dimensionally reduced d = 1 + 1 Weyl supersymmetric and Majorana supersymmetric electrodynamics.     

Dynamics of loops in superspace

The loop equation, analogous to the Makeenko-Migdal equation, is derived for the supersymmetric generalization of the Wilson loop for the supersymmetric (N = 1) gauge theory.     

Factorization of Integrals Defining the β-Function into Integrals of Total Derivatives in N=1 SQED, Regularized by Higher Derivatives

Some calculations in supersymmetric theories, made with the higher derivative regularization, show that the β-function is given by integrals of total derivatives. This is qualitatively explained for the N=1 supersymmetric electrodynamics in all orders.     

Supergraphity: (II). Manifestly covariant rules and higher-loop finiteness

We continue our discussion of the background field formalism in supersymmetric theories, deriving new covariant Feynman rules for chiral superfields. As a result, we obtain improved power-counting rules for both simple and extended supersymmetry which can be used to make the following statements: If the corresponding extended superfield formalism exist, (a) N=2 supersymmetric Yang-Mills theory is finite beyond one loop, (b) N=4 Yang-Mills is finite at all loops, and (c) N=8 supergravity is finite through six loops. We also find that in simple super-Yang-Mills the radiative corrections to the Fayet-Iliopoulos (“D”) term, which are known to vanish for higher loops, also vanish automatically at one loop for arbitrary couplings.     

Integrability and Seiberg-Witten theory curves and periods

The interpretation of exact results on the low-energy limit of 4D N = 2 supersymmetric Yang-Mills theory in the language of 1D integrable system of particles is discussed. The Riemann surfaces of the Seiberg-Witten theory are explicitly described as spectral curves of Lax operators. The case of the elliptic Calogero system, associated with the flow between N = 4 and N = 2 supersymmetric in 4D, is considered in some detail. Equations for the corresponding Riemann surfaces are written down rather explicitly for all the SU(n) groups.