On low rank classical groups in string theory, gauge theory and matrix models

Abstract

We consider N = 1 supersymmetric U (N ), SO(N ), and Sp(N ) gauge theories, with two-index tensor matter and added tree-level superpotential, for general breaking patterns of the gauge group. By considering the string theory realization and geometric transitions, we clarify when glueball superfields should be included and extremized, or rather set to zero; this issue arises for unbroken group factors of low rank. The string theory results, which are equivalent to those of the matrix model, refer to a particular UV completion of the gauge theory, which could differ from conventional gauge theory results by residual instanton effects. Often, however, these effects exhibit miraculous cancellations, and the string theory or matrix model results end up agreeing with standard gauge theory. In particular, these string theory considerations explain and remove some apparent discrepancies between gauge theories and matrix models in the literature.

Nonsupersymmetric flux vacua and perturbed 𝒩 = 2 systems

“…A more efficient method amenable to computer was proposed in [85,86,87], and here we generalize it to the case with an arbitrary number of cuts n. First note that the perturbative part of the matrix model free energy F mm can be written as an expansion in the coupling constant g s as: Here, the order k amplitude f k (N) is a polynomial of degree k + 2 in N i 's, which in turn has a genus expansion as follows: This symmetry significantly reduces the number of "data points" {N i }, for which we should evaluate the matrix integral in order to determine f k (N). In particular, this means that, if one knows f k (N) for n = k + 2 cuts, then one can determine f k (N) for arbitrary number of cuts n by symmetry.…”

On Nonperturbative Exactness of Konishi Anomaly and the Dijkgraaf-Vafa Conjecture

“…Similar relations for the Sp(N ) and SO(N ) gauge theory are given in [14] and [7]. The derivation of the relation (9.6) rests on the Konishi anomaly equations and on the validity of low energy description of the gauge theory in terms of the glueball fields S i .…”

“…Such corrections are expected due to ambiguities in the definition of highly nonrenormalizable operators like Tr Φ n [7]- [9]. We show that all the ambiguities can be absorbed into nonperturbative redefinition of the superpotential.…”

“…In particular we show nonrenormalization of the generalized Konishi anomaly for SO(N ) and Sp(N ) gauge theories with matter in the symmetric or antisymmetric representation. The nonrenormalization of the generalized Konishi anomaly for Sp(N ) with the antisymmetric tensor is expected in the light of recent results [10] and [7] that demonstrated agreement between the effective superpotential obtained using Konishi anomalies with the dynamically generated superpotential approach [11,12]. The papers [10] and [7] resolved a puzzle raised in [13]- [15] about the application of Dijkgraaf-Vafa correspondence for Sp(N ) with antisymmetric matter.…”

More onN=1 Matrix Model Curve for ArbitraryN

“…In other words, the glueball approach is not allowed. 29 • SO (5) with N f = 1: Non-baryonic r = 0 branch To see the equivalence between two approaches easily, we solve the factorization again by using the following parametrization,…”