S. Yankielowicz

An Effective Lagrangian for the Pure N=1 Supersymmetric Yang-Mills Theory

Abstract An effective lagrangian for the pure, N =1, supersymmetric Yang-Mills theory is proposed by suitably modifying that of QCD. The quantum breaking of scale and chiral invariance by the corresponding anomalies generates a massive Wess-Zumino supermultiplet while preserving supersymmetry. The large- N c limit is discussed for an SU ( N c ) gauge group.

Simple singularities and N = 2 supersymmetric Yang-Mills theory

We present a first step towards generalizing the work of Seiberg and Witten on N = 2 supersymmetric Yang-Mills theory to arbitrary gauge groups. Specifically, we propose a particular sequence of hyperelliptic genus n - 1 Riemann surfaces to underly the quantum moduli space of W(n) N = 2 supersymmetric gauge theory. These curves have an obvious generalization to arbitrary simply laced gauge groups, which involves the A-D-E type simple singularities. To support our proposal, we argue that the monodromy in the semiclassical regime is correctly reproduced. We also give some remarks on a possible relation to string theory.

Extended Chiral Algebras and Modular Invariant Partition Functions

We show how the fusion rules can be used to associate with every rational conformal field theory a discrete group, the center. The center is generated by primary fields having unique fusion rules with any other field. The existence of a non-trivial center implies the existence of non-diagonal modular invariants, which are related to extended integer or fractional spin algebras. Applied to Kac-Moodt algebras this method yields all known as well as many new infinite series of modular invariants. Some results on exceptional invariants are also presented, including an example of an exceptional integer spin invariant that does not correspond to a conformal embedding.

Field identification fixed points in the coset construction

Abstract We discuss two related problems in conformal field theory. The first is the construction of the modular transformation matrix S for integer spin modular invariants in which some characters appear with multiplicity larger than 1. The second problem is the relation between the characters and the branching functions in coset theories in which the field identification identifies some fields with themselves (“fixed points”). We find that these problems are closely related, and that the solution is remarkably interesting. The fixed points of any conformal field theory seem always to define a new (not necessarily unitary) conformal field theory whose primary fields are in one-to-one correspondence with the fixed points. The characters of this conformal field theory are needed to modify the coset branching functions.

Modular invariants from simple currents. An explicit proof

Abstract In a previous paper an orbifold construction was used to demonstrate that the existence of primary fields with simple fusion rules in a conformal field theory implies the existence of non-diagonal modular invariant partition functions. Here we present a direct and explicit proof of modular invariance, which also covers a few cases that could not be obtained with the orbifold method. We also give a very simple general formula for the modular matrix M .

New modular invariants for N = 2 tensor products and four-dimensional strings

Abstract The construction of modular invariant partition functions of tensor products of N = 2 superconformal field theories is clarified and extended by means of a recently proposed method using simple currents, i.e. primary fields with simple fusion rules. Apart from providing a conceptually much simpler way of understanding space-time and world-sheet supersymmetry projections in modular invariant string theories, this makes a large class of modular invariant partition functions accessible for investigation. We demonstrate this by constructing thousands of (2, 2), (1, 2) and (0, 2) string theories in four dimensions, including more than 40 new three generation models.

Exotic nonsupersymmetric gauge dynamics from supersymmetric QCD.

We extend Seiberg`s qualitative picture of the behavior of supersymmetric QCD to nonsupersymmetric models by adding soft supersymmetry-breaking terms. In this way we recover the standard vacuum of QCD with {ital N}{sub {ital f}} flavors and {ital N}{sub {ital c}} colors when {ital N}{sub {ital f}}{lt}{ital N}{sub {ital c}}. However, for {ital N}{sub {ital f}}{ge}{ital N}{sub {ital c}}, we find new exotic states---new vacua with spontaneously broken baryon number for {ital N}{sub {ital f}}={ital N}{sub {ital c}}, and a vacuum state with unbroken chiral symmetry for {ital N}{sub {ital f}}{gt}{ital N}{sub {ital c}} These exotic vacua contain massless composite fermions and, in some cases, dynamically generated gauge bosons. In particular Seiberg`s electric-magnetic duality seems to persist also in the presence of (small) soft supersymmetry breaking. We argue that certain, specially tailored, lattice simulations may be able to detect the novel phenomena. Most of the exotic behavior does not survive the decoupling limit of large SUSY-breaking parameters.

Physical states in G/G models and two-dimensional gravity

Abstract An analysis of the BRST cohomology of the G/G topological models is performed for the case of A 1 (1) . Invoking a special free field parametrization of the various currents, the cohomology on the corresponding Fock space is extracted. We employ the singular vector structure and fusion rules to translate the latter into the cohomology on the space of irreducible representations. Using the physical states we calculate the characters and partition function, and verify the index interpretation. We twist the energy-momentum tensor to establish an intriguing correspondence between the SL(2)/SL(2) model with level k = p / q −2 and ( p , q ) models coupled to gravity.

CURIOSITIES AT c = 24

Abstract Two examples of c =24 holomorphic conformal field theories are given that do not correspond to Niemeier lattices or Z 2 twists of Niemeier lattices. One of these examples clarifies a recently discovered modular invariant of F 4 at level 6, which can be interpreted as the “complement” of SU(3) level 2 within a new c =24 theory.

Flows and duality symmetries in N = 1 supersymmetric gauge theories

We present more examples of dual N = 1 SUSY gauge theories. This set of theories is connected by flows to both Seibergs and Kutasovs dual theories. This provides a unifying picture of the various dual theories. We investigate the dual theories, their flat directions and mass perturbations.