Showing papers on "Supersymmetric gauge theory published in 1997"

Lectures on supersymmetric gauge theories and electric-magnetic duality

Abstract: We review some of the recent work on the dynamics of four dimensional, supersymmetric gauge theories. The kinematics are largely determined by holomorphy and the dynamics are governed by duality. The results shed light on the phases of gauge theories. Some results and interpretations which have not been published before are also included.

Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories

Abstract: For quantum field theories that flow between ultraviolet and infrared fixed points, central functions, defined from two-point correlators of the stress tensor and conserved currents, interpolate between central charges of the UV and IR critical theories. We develop techniques that allow one to calculate the flows of the central charges and that of the Euler trace anomaly coefficient in a general N=1 supersymmetric gauge theory. Exact, explicit formulas for $SU(N_c)$ gauge theories in the conformal window are given and analysed. The Euler anomaly coefficient always satisfies the inequality $% a_{UV}-a_{IR}>0$. This is new evidence in strongly coupled theories that this quantity satisfies a four-dimensional analogue of the $c$-theorem, supporting the idea of irreversibility of the RG flow. Various other implications are discussed.

Five-Dimensional Supersymmetric Gauge Theories and Degenerations of Calabi-Yau Spaces

Abstract: We discuss five-dimensional supersymmetric gauge theories. An anomaly renders some theories inconsistent and others consistent only upon including a Wess-Zumino type Chern-Simons term. We discuss some necessary conditions for existence of nontrivial renormalization group fixed points and find all possible gauge groups and matter content which satisfy them. In some cases, the existence of these fixed points can be inferred from string duality considerations. In other cases, they arise from M-theory on Calabi-Yau threefolds. We explore connections between aspects of the gauge theory and Calabi-Yau geometry. A consequence of our classification of field theories with nontrivial fixed points is a fairly complete classification of a class of singularities of Calabi-Yau threefolds which generalize the ``del Pezzo contractions'' and occur at higher codimension walls of the K\"{a}hler cone.

Perturbations of spacetime : gauge transformations and gauge invariance at second order and beyond

Abstract: We consider in detail the problem of gauge dependence that exists in relativistic perturbation theory, going beyond the linear approximation and treating second- and higher-order perturbations. We first derive some mathematical results concerning the Taylor expansion of tensor fields under the action of one-parameter families (not necessarily groups) of diffeomorphisms. Secondly, we define gauge invariance to an arbitrary order n. Finally, we give a generating formula for the gauge transformation to an arbitrary order and explicit rules to second and third order. This formalism can be used in any field of applied general relativity, such as cosmological and black hole perturbations, as well as in other spacetime theories. As a specific example, we consider here second-order perturbations in cosmology, assuming a flat Robertson - Walker background, giving explicit second-order transformations between the synchronous and the Poisson (generalized longitudinal) gauges.

Gauge fields in the separation of rotations and internal motions in the n-body problem

Abstract: The problem of separating rotations from internal motions in systems such as macroscopic flexible bodies, atoms, molecules, nuclei, and solar systems is an old one, with many applications in physics, chemistry, and engineering. A new element, however, which has not been appreciated until fairly recently, is the existence of certain gauge fields on the reduced configuration space for such systems. These (non-Abelian) gauge fields arise in the ``falling cat'' problem, in which changes in shape induce changes in external orientation; but they also have a dynamical significance, and enter as gauge potentials in the Lagrangian or Hamiltonian describing the internal or reduced dynamics. Physically these gauge fields represent Coriolis effects. This review concentrates on the case of nonrelativistic, n-body systems not subject to external torques, and develops the gauge theory of rotations and internal motions in detail. Both classical and quantum treatments are given. The gauge theory is developed from the standpoint of classical, coordinate-based tensor analysis; more abstract mathematical notation is generally not used, although the basic geometrical ideas of fiber-bundle theory are developed as needed. Certain old results, such as the Wilson-Howard-Watson Hamiltonian of molecular physics, are examined from a gauge-theoretical standpoint; and several new results are presented, including field equations of the Kaluza-Klein type satisfied by the gauge fields, and geometrical interpretations of the Eckart frame.

The dawning of gauge theory

Abstract: During the course of this century, gauge invariance has slowly emerged from being an incidental symmetry of electromagnetism to being a fundamental geometrical principle underlying the four known fundamental physical interactions. The development has been in two stages. In the first stage (1916-1956), the geometrical significance of gauge-invariance gradually came to be appreciated and the original abelian gauge-invariance of electromagnetism was generalized to non-abelian gauge-invariance. In the second stage (1960-1975), it was found that, contrary to first appearances, the non-abelian gauge-theories provided exactly the framework that was needed to describe the nuclear interactions (both weak and strong) and thus provided a universal framework for describing all known fundamental interactions. This book describes the first phase of the development. The author first illustrates how gravitational theory and quantum mechanics played crucial roles in the reassessment of gauge theory as a geometric principle and as a framework for describing both electromagnetism and gravitation. He then describes how the abelian electromagnetic gauge-theory was generalized to its present non-abelian form. The development is illustrated by including a selection of relevant articles, many of them appearing for the first time in English. The articles illustrate that the reassessment of gauge-theory, due to in a large measure to Weyl, constituted a major philosophical as well as technical advances.

Non-abelian bogomol'nyi-prasad-sommerfield monopoles in n = 4 gauged supergravity

Abstract: We study static, spherically symmetric, and purely magnetic solutions of SU(2){times}SU(2) gauge supergravity in four dimensions. A systematic analysis of the supersymmetry conditions reveals solutions which preserve 1/4 of the supersymmetries and are characterized by a BPS-monopole-type gauge field and a globally hyperbolic, everywhere regular geometry. These present the first known example of non-Abelian backgrounds in gauge supergravity and in leading order effective string theory. {copyright} {ital 1997} {ital The American Physical Society}

Introduction to S duality in N=2 supersymmetric gauge theories: A Pedagogical review of the work of Seiberg and Witten

Abstract: In these notes we attempt to give a pedagogical introduction to the work of Seiberg and Witten on S-duality and the exact results of N = 2 supersymmetric guage theories with and without matter. The first half is devoted to a review of monopoles in guage theories and the construction of supersymmetric guage theories. In the second half, we describe the work of Seiberg and Witten.

Field Theory on a Supersymmetric Lattice

Abstract: A lattice-type regularization of the supersymmetric field theories on a supersphere is constructed by approximating the ring of scalar superfields by an integer-valued sequence of finite dimensional rings of supermatrices and by using the differencial calculus of non-commutative geometry. The regulated theory involves only finite number of degrees of freedom and is manifestly supersymmetric.

On the integrable geometry of soliton equations and $N=2$ supersymmetric gauge theories

Abstract: We provide a unified construction of the symplectic forms which arise in the solution of both N=2 supersymmetric Yang-Mills theories and soliton equations. Their phase spaces are Jacobian-type bundles over the leaves of a foliation in a universal configuration space. On one hand, imbedded into finite-gap solutions of soliton equations, these symplectic forms assume explicit expressions in terms of the auxiliary Lax pair, expressions which generalize the well-known Gardner-Faddeev-Zakharov bracket for KdV to a vast class of 2D integrable models; on the other hand, they determine completely the effective Lagrangian and BPS spectrum when the leaves are identified with the moduli space of vacua of an N=2 supersymmetric gauge theory. For SU($N_c$) with $N_f\leq N_c+1$ flavors, the spectral curves we obtain this way agree with the ones derived by Hanany and Oz and others from physical considerations.

Strong coupling dynamics of four-dimensional $N = 1$ gauge theories from M-theory fivebrane

Abstract: It has been known that the fivebrane of type IIA theory can be used to give an exact low energy description of N=2 supersymmetric gauge theories in four dimensions. We follow the recent M theory description by Witten and show that it can be used to study theories with N=1 supersymmetry. The N=2 supersymmetry can be broken to N=1 by turning on a mass for the adjoint chiral superfield in the N=2 vector multiplet. We construct the configuration of the fivebrane for both finite and infinite values of the adjoint mass. The fivebrane describes strong coupling dynamics of N=1 theory with SU(N_c) gauge group and N_f quarks. For N_c > N_f, we show how the brane configuration encodes the information of the Affleck-Dine-Seiberg superpotential. For N_c = and < N_f, we study the deformation space of the brane configuration and compare it with the moduli space of the N=1 theory. We find agreement with field theory results, including the quantum deformation of the moduli space at N_c = N_f. We also prove the type II s-rule in M theory and find new non-renormalization theorems for N=1 superpotentials.

Introduction to S-Duality in N=2 Supersymmetric Gauge Theory. (A pedagogical review of the work of Seiberg and Witten)

Abstract: In these notes we attempt to give a pedagogical introduction to the work of Seiberg and Witten on S-duality and the exact results of N=2 supersymmetric gauge theories with and without matter. The first half is devoted to a review of monopoles in gauge theories and the construction of supersymmetric gauge theories. In the second half, we describe the work of Seiberg and Witten.