Generalized Konishi anomaly, Seiberg duality and singular effective superpotentials

Using the generalized Konishi anomaly (GKA) equations, we derive the effective superpotential of four-dimensional N=1 supersymmetric SU(n) gauge theory with n+2 fundamental flavors. We find, however, that the GKA equations are only integrable in the Seiberg dual description of the theory, but not in the direct description of the theory. The failure of integrability in the direct, strongly coupled, description suggests the existence of non-perturbative corrections to the GKA equations.Comment: 20 pages; v3: corrected the comparison to the SU(2) cas

On the next-to-leading-order correction to the effective action in N=2 gauge theories

I attempt to analyse the next-to-leading-order non-holomorphic contribution to the Wilsonian low-energy effective action in the four-dimensional N=2 gauge theories with matter, from the manifestly N=2 supersymmeric point of view, by using the harmonic superspace. The perturbative one-loop correction is found to be in agreement with the N=1 superfield calculations of de Wit, Grisaru and Rocek. The previously unknown coefficient in front of this non-holomorphic correction is calculated. A special attention is devoted to the N=2 superconformal gauge theories, whose one-loop non-holomorphic contribution is likely to be exact, even non-perturbatively. This leading (one-loop) non-holomorphic contribution to the LEEA of the N=2 superconformally invariant gauge field theories is calculated, and it does not vanish, similarly to the case of the N=4 super-Yang-Mills theory.Comment: 15 pages, LaTeX; changes in the abstract and in sect.

On the Moduli Space of N = 2 Supersymmetric G_2 Gauge Theory

We apply the method of confining phase superpotentials to N = 2 supersymmetric Yang-Mills theory with the exceptional gauge group G_2. Our findings are consistent with the spectral curve of the periodic Toda lattice, but do not agree with the hyperelliptic curve suggested previously in the literature. We also apply the method to theories with fundamental matter, treating both the example of SO(5) and G_2.Comment: 14 pages, LaTeX, 1 figure, reference adde

On singular effective superpotentials in supersymmetric gauge theories

We study N=1 supersymmetric SU(2) gauge theory in four dimensions with a large number of massless quarks. We argue that effective superpotentials as a function of local gauge-invariant chiral fields should exist for these theories. We show that although the superpotentials are singular, they nevertheless correctly describe the moduli space of vacua, are consistent under RG flow to fewer flavors upon turning on masses, and also reproduce by a tree-level calculation the higher-derivative F-terms calculated by Beasely and Witten (hep-th/0409149) using instanton methods. We note that this phenomenon can also occur in supersymmetric gauge theories in various dimensions.Comment: 21 pages, 5 figures; minor errors correcte

New Jacobi-Like Identities for Z_k Parafermion Characters

We state and prove various new identities involving the Z_K parafermion characters (or level-K string functions) for the cases K=4, K=8, and K=16. These identities fall into three classes: identities in the first class are generalizations of the famous Jacobi theta-function identity (which is the K=2 special case), identities in another class relate the level K>2 characters to the Dedekind eta-function, and identities in a third class relate the K>2 characters to the Jacobi theta-functions. These identities play a crucial role in the interpretation of fractional superstring spectra by indicating spacetime supersymmetry and aiding in the identification of the spacetime spin and statistics of fractional superstring states.Comment: 72 pages (or 78/2 = 39 pages in reduced format

Multiparticle tree amplitudes in scalar field theory

Following an argument advanced by Feynman, we consider a method for obtaining the effective action which generates the sum of tree diagrams with external physical particles. This technique is applied, in the unbroken \lambda \phi^4 theory, to the derivation of the threshold amplitude for the production of $n$ scalar particles by $n$ initial particles. The leading contributions to the tree amplitude, which become singular in the threshold limit, exhibit a factorial growth with n.Comment: uuencoded gz-compressed file created by csh script uufile

Singularities of N=1 Supersymmetric Gauge Theory and Matrix Models

In N=1 supersymmetric U(N) gauge theory with adjoint matter $\Phi$ and polynomial tree-level superpotential $W(\Phi)$, the massless fluctuations about each quantum vacuum are generically described by $U(1)^n$ gauge theory for some n. However, by tuning the parameters of $W(\Phi)$ to non-generic values, we can reach singular vacua where additional fields become massless. Using both the matrix model prescription and the strong-coupling approach, we study in detail three examples of such singularities: the singularities of the n=1 branch, intersections of n=1 and n=2 branches, and a class of N=1 Argyres-Douglas points. In all three examples, we find that the matrix model description of the low-energy physics breaks down in some way at the singularity.Comment: 29 pages, 1 figure. Revised section 1, fixed misprints in section 3.1, added clarifications and reference

Rigid surface operators and S-duality: some proposals

We study surface operators in the N=4 supersymmetric Yang-Mills theories with gauge groups SO(n) and Sp(2n). As recently shown by Gukov and Witten these theories have a class of rigid surface operators which are expected to be related by S-duality. The rigid surface operators are of two types, unipotent and semisimple. We make explicit proposals for how the S-duality map should act on unipotent surface operators. We also discuss semisimple surface operators and make some proposals for certain subclasses of such operators.Comment: 27 pages. v2: minor changes, added referenc

Argyres-Douglas theories and S-duality

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are creditedM.B. and T.N. are partly supported by the U.S. Department of Energy under grants DOE-SC0010008, DOE-ARRA-SC0003883, and DOE-DE-SC0007897. This research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915. S.G. is partially supported by the ERC Advanced Grant “SyDuGraM”, by FNRS-Belgium (convention FRFC PDR T.1025.14 and convention IISN 4.4514.08) and by the “Communaut´e Francaise de Belgique” through the ARC progra

General Argyres-Douglas Theory

We construct a large class of Argyres-Douglas type theories by compactifying six dimensional (2,0) A_N theory on a Riemann surface with irregular singularities. We give a complete classification for the choices of Riemann surface and the singularities. The Seiberg-Witten curve and scaling dimensions of the operator spectrum are worked out. Three dimensional mirror theory and the central charges a and c are also calculated for some subsets, etc. Our results greatly enlarge the landscape of N=2 superconformal field theory and in fact also include previous theories constructed using regular singularity on the sphere.Comment: 55 pages, 20 figures, minor revision and typos correcte