Quantum Moduli Space Of Vacua Research Articles

Aspects of N = 2 supersymmetric gauge theories in three dimensions

We consider general aspects of N = 2 gauge theories in three dimensions, including their multiplet structure, anomalies and non-renormalization theorems. For U (1) gauge theories, we discuss the quantum corrections to the moduli space, and their relation to “mirror symmetries” of 3d N = 4 theories. Mirror symmetry is given an interpretation in terms of vortices. For SU ( N c ) gauge groups with N f fundamental flavors, we show that, depending on the number of flavors, there are quantum moduli spaces of vacua with various phenomena near the origin.

Integrable Models, SUSY Gauge Theories and String Theory

We consider the close relation between duality in N = 2 SUSY gauge theories and integrable models. Various integrable models ranging from Toda lattices, Calogero models, spinning tops, and spin chains are related to the quantum moduli space of vacua of N = 2 SUSY gauge theories. In particular, SU(3) gauge theories with two flavors of massless quarks in the fundamental representation can be related to the spectral curve of Goryachev–Chaplygin top, which is a Nahm's equation in disguise. This can be generalized to the cases with massive quarks, and Nf = 0,1,2, where a system with seven dimensional phase space has the relevant hyperelliptic curve appear in the Painlevè test. To understand the string origin of the integrability of these theories we obtain exact nonperturbative point particle limit of type II string compactified on a Calabi–Yau manifold, which gives the hyperelliptic curve of SU(2) QCD with Nf = 1 hypermultiplet.

Integrable structure in supersymmetric gauge theories with massive hypermultiplets

We study the quantum moduli space of vacua of N = 2 supersymmetric SU( N c ) gauge theories coupled to N f flavors of quarks in the fundamental representation. We identify the moduli space of the N c = 3 and N f = 2 massless case with the full spectral curve obtained from the Lax representation of the Goryachev-Chaplygin top. For the case with massive quarks, we present an integrable system where the corresponding hyperelliptic curve parametrizing the Laurent solution coincides with that of the moduli space of N c = 3 with N f = 0, 1, 2. We discuss possible generalizations of the integrable systems relevant to gauge theories with N c ≠ 3 and general N f .

On the quantum moduli space of vacua of N = 2 supersymmetric gauge theories

Families of hyper-elliptic curves which describe the quantum moduli spaces of vacua of N = 2 supersymmetric SO( N c ) gauge theories coupled to N f flavors of quarks in the vector representation are constructed. The quantum moduli spaces for 2 N f < N c − 1 are determined completely by imposing R-symmetry, instanton corrections and the proper classical singularity structure. These curves are verified by residue calculations. The quantum moduli spaces for 2 N f ⩾ N c − 1 theories are parameterized and their general structure is worked out using residue calculations. The exact metrics on the quantum moduli spaces as well as the exact spectrum of stable massive states are derived. The results presented here together with recent results of Martinec and Warner provide a natural conjecture for the form of the curves for the other gauge groups.

On the quantum moduli space of vacua of N = 2 supersymmetric SU( Nc) gauge theories

We construct families of hyper-elliptic curves which describe the quantum moduli spaces of vacua of N = 2 supersymmetric SU( N c ) gauge theories coupled to N f flavors of quarks in the fundamental representation. The quantum moduli spaces for N f < N c are determined completely by imposing R-symmetry, instanton corrections and the proper classical singularity structure. These curves are verified by residue and weak coupling monodromy calculations. The quantum moduli spaces for N f ⩾ N c theories are parameterized and their general structure is worked out using residue calculations. Global symmetry considerations suggest a complete description of them. The results are supported by weak coupling monodromy calculations. The exact metrics on the quantum moduli spaces as well as the exact spectrum of stable massive states are derived. We find an example of a novel symmetry of a quantum moduli space: Invariance under the exchange of a moduli parameter and the bare mass. We apply our method for the construction of the quantum moduli spaces of vacua of N = 1 supersymmetric theories in the Coulomb phase.

Exact superpotentials, quantum vacua and duality in supersymmetric SP( Nc) gauge theories

We study N = 1 supersymmetric SP( N c ) gauge theories with N f flavors of quarks in the fundamental representation. Depending on N f and N c , we find exact, dynamically generated superpotentials, smooth quantum moduli spaces of vacua, quantum moduli spaces of vacua with additional massless composites at strong coupling, confinement without chiral symmetry breaking, non-trivial fixed points of the renormalization group, and massless magnetic quarks and gluons.