Moduli Space Of Vacua Research Articles

Deformed Matrix Theories with Script N = 8 and Fivebranes in the PP Wave Background

M(atrix) theory is known to be mass-deformed in the pp-wave background and still retains all 16 dynamical supersymmetries. We consider generalization of such deformations on super Yang-Mills quantum mechanics (SYQM) with less supersymmetry. In particular this includes N=8 U(N) SYQM with a single adjoint and any number of fundamental hypermultiplets, which is a pp-wave deformation of DLCQ matrix theory of fivebranes. With k >= 1 fivebranes, we show that a rich vacuum structure exists, with many continuous family of solutions that preserve all dynamical supersymmetries. The vacuum moduli space contains copies of CP^{k-1} of various sizes.

MARGINAL DEFORMATIONS OF N=4 SYM AND NON-COMMUTATIVE MODULI SPACES OF VACUA

We review recent work on the application of the non-commutative geometric framework to an interpretation of the moduli space of vacua of marginal deformations of N = 4 super Yang-Mills theories. At rational values of couplings, different regions of moduli space may be associated with D5-branes of various topologies, and orbifold dual descriptions exist which may be accessed by T-duality. Singularities in the moduli space are associated with topology change.

Monopole dynamics and BPS dyons inN=2super-Yang-Mills theories

We determine the low-energy dynamics of monopoles in pure $N=2$ Yang-Mills theories for points in the vacuum moduli space where the two Higgs fields are not aligned. The dynamics is governed by a supersymmetric quantum mechanics with potential terms and four real supercharges. The corresponding superalgebra contains a central charge but nevertheless supersymmetric states preserve all four supercharges. The central charge depends on the sign of the electric charges and consequently so does the BPS spectrum. We focus on the SU(3) case where certain BPS states are realized as zero modes of a Dirac operator on Taub-NUT space twisted by the triholomorphic Killing vector field. We show that the BPS spectrum includes hypermultiplets that are consistent with the strong- and weak-coupling behavior of Seiberg-Witten theory.

Compactified little string theories and compact moduli spaces of vacua

It is emphasized that compactified little string theories have compact moduli spaces of vacua, which globally probe compact string geometry. Compactifying various little string theories on T^3 leads to 3d theories with exact, quantum Coulomb branch given by: an arbitrary T^4 of volume M_s^2, an arbitrary K3 of volume M_s^2, and moduli spaces of G=SU(N), SO(2N), or E_{6,7,8} instantons on an arbitrary T^4 or K3 of fixed volume. Compactifying instead on a T^2 leads to 4d theories with a compact Coulomb branch base which, when combined with the exact photon gauge coupling fiber, is a compact, elliptically-fibered space related to the above spaces.

The light spectrum near the Argyres–Douglas point

We consider N=2 super Yang-Mills theory with SU(2) gauge group and a single quark hypermultiplet in the fundamental representation. For a specific value of the quark bare mass and at a certain point in the moduli space of vacua, the central charges corresponding to two mutually non-local electro-magnetic charges vanish simultaneously, indicating the possibility of massless such states in the spectrum. By realizing the theory as an M-theory configuration, we show that these states indeed exist in the spectrum near the critical point.

On the twisted (2, 0) and little-string theories

We study the compactification of the (2, 0) and type-II little-string theories on S 1, T 2 and T 3 with an R-symmetry twist that preserves half the supersymmetry. We argue that it produces the same moduli spaces of vacua as compactification of the (1, 0) theory with E 8 Wilson lines given by a maximal embedding of SU(2). In certain limits, this reproduces the moduli space of SU(2) with a massive adjoint hyper-multiplet. In the type-II little-string theory case, we observe a peculiar phase transition where the strings condense. We conjecture a generalization to more than two 5-branes which involves instantons on non-commutative T 4. We conclude with open questions.

Partition functions, duality and the tube metric

The partition function of type IIA and B strings on R 6 × K3 , in the T 4/ Z 2 orbifold limit, is explicitly computed as a modular invariant sum over spin structures required by perturbative unitarity in order to extend the analysis to include type II strings on R6 × W4 , where W4 is associated with the tube metric conformal field theory, given by the degrees of freedom transverse to the Neveu-Schwarz fivebrane solution. This generates partition functions and perturbative spectra of string theories in six space-time dimensions, associated with the modular invariants of the level- k affine SU(2) Kac-Moody algebra. These theories provide a conformal field theory (i.e. perturbative) probe of non-perturbative (fivebrane) vacua. We contrast them with theories whose N = (4, 4) sigma-model action contains n H = k + 2 hypermultiplets as well as vector supermultiplets, and where k is the level just mentioned. In Appendix B we also give a D = 6, N = (1, 1) ‘free fermion’ string model which has. a different moduli space of vacua from the 81-parameter space relevant to the above examples.

Dyon electric charge and fermion fractionalization in N = 2 gauge theory

A first principles calculation of the quantum corrections to the electric charge of a dyon in an N = 2 gauge theory with arbitrary gauge group is presented. These corrections arise from the fermion fields via the mechanism of fermion fractionalization. For a dyon whose magnetic charge is a non-simple co-root, the correction is a discontinuous function on the moduli space of vacua and the discontinuities occur precisely on co-dimension-I curves on which the dyon decays. In this way, the complete spectrum of dyons at weak coupling is found for a theory with any gauge group. It is shown how this spectrum is consistent with the semi-classical monodromies.

Aspects of N=1 string dynamics

We review several topics of interest in the study of 4d N=1 supersymmetric compactifications of the heterotic string. After a brief introduction to the construction of such models, our focus is on the novel physics which occurs at singularities in the moduli space of vacua. Among the phenomena we discuss are nonperturbative superpotentials, dynamical generation of poles in various low-energy couplings, and phase transitions which change the net number of chiral generations.

SUSY gauge dynamics and singularities of 4d N = 1 string vacua

Many N = 1 heterotic string compactifications exhibit physically mysterious singularities at codimension one in the moduli space of vacua. At these singularities, Yukawa couplings of charged fields develop poles as a function of the moduli. We explain these conformal field theory singularities, in a class of examples, as arising from non-perturbative gauge dynamics of non-perturbative gauge bosons (whose gauge coupling is the sigma model coupling) in the string theory.

Discontinuous BPS spectra in N = 2 gauge theory

We consider the spectrum of BPS saturated states in N = 2 gauge theories in four dimensions. This spectrum may be discontinuous across real codimension one submanifolds of marginal stability in the moduli space of vacua. An example, which can be treated with semiclassical methods in the weak coupling limit, is the decay of quark-soliton bound states. For a quark and a soliton of electric-magnetic charge vectors Q and Q′ respectively, we find that as the manifold of marginal stability is crossed, the number of soliton states changes by a factor of 2 Q·Q′ where the dot denotes the symplectic product.

Exact supersymmetric massive and massless white holes.

We study special points in the moduli space of vacua at which supersymmetric electric solutions of the heterotic string theory become massless. We concentrate on configurations for which supersymmetric non-renormalization theorem is valid. Those are ten-dimensional supersymmetric string waves and generalized fundamental strings with SO(8) holonomy group. From these we find the four dimensional spherically symmetric configurations which saturate the BPS bound, in particular near the points of the vanishing ADM mass. The non-trivial massless supersymmetric states in this class exist only in the presence of non-Abelian vector fields.We also find a new class of supersymmetric massive solutions, closely related to the massless ones. A distinctive property of all these objects, either massless or massive, is the existence of gravitational repulsion. They reflect all particles with nonvanishing mass and/or angular momentum, and therefore they can be called white holes (repulsons), in contrast to black holes which tend to absorb particles of all kinds. If such objects can exist, we will have the first realization of the universal gravitational force which repels all particles with the strength proportional to their mass and therefore can be associated with antigravity.

Vacuum Structure and Spectrum ofN=2SupersymmetricSU(n)Gauge Theory

We present an exact description of the metric on the moduli space of vacua and the spectrum of massive states for four dimensional N=2 supersymmetric SU(n) gauge theories. The moduli space of quantum vacua is identified with the moduli space of a special set of genus n-1 hyperelliptic Riemann surfaces.

Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory

We study the vacuum structure and don spectrum of N=2 supersymmetric gauge theory in four dimensions, with gauge group SU(2). The theory turns out to have remarkably rich and physical properties which can nonetheless be described precisely; exact formulas can be obtained, for instance, for electron and dyon masses and the metric on the moduli space of vacua. The description involves a version of Olive-Montonen electric-magnetic duality. The “strongly coupled” vacuum turns out to be a weakly coupled theory of monopoles, and with a suitable perturbation confinement is described by monopole condensation.

Exact results on the space of vacua of four-dimensional SUSY gauge theories.

We consider four dimensional quantum field theories which have a continuous manifold of inequivalent exact ground states -- a moduli space of vacua. Classically, the singular points on the moduli space are associated with extra massless particles. Quantum mechanically these singularities can be smoothed out. Alternatively, new massless states appear there. These may be the elementary massless particles or new massless bound states.