Simple singularities and N = 2 supersymmetric Yang-Mills theory

We consider four-dimensional N = 2 supersymmetric gauge theories with gauge group U (N ) on R 3 ×S 1 , in the presence of a classical superpotential. The low-energy quantum superpotential is obtained by simply replacing the adjoint scalar superfield in the classical superpotential by the Lax matrix of the integrable system that underlies the 4d field theory. We verify in a number of examples that the vacuum structure obtained in this way matches precisely that in 4d, although the degrees of freedom that appear are quite distinct. Several features of 4d field theories, such as the possibility of lifting vacua from U (N ) to U (tN ), become particularly simple in this framework. It turns out that supersymmetric vacua give rise to a reduction of the integrable system which contains information about the field theory but also about the Dijkgraaf-Vafa matrix model. The relation between the matrix model and the quantum superpotential on R 3 × S 1 appears to involve a novel kind of mirror symmetry.

Section: N = 2 Deformations In D =supporting

confidence: 68%

Section: U (2)mentioning

confidence: 99%

See 1 more Smart Citation

Nonperturbative Superpotentials and Compactification to Three Dimensions

Boels¹,

Duivenvoorden²,

Wijnhout³

2004

“…In particular, the SU(N) Seiberg-Witten curve of gauge theory [48,49] is geometrically identified with the curve (3.14) underlying the Calabi-Yau. A T -duality along the compact circle in the uv-fiber, followed by a lift to M-theory, translates [50] this geometry into a system of an M5-brane which wraps the Riemann surface Σ SW and fills R 3,1 .…”

Section: Seiberg-witten Geometriesmentioning

confidence: 99%

Nonsupersymmetric flux vacua and perturbed 𝒩 = 2 systems

Hollands¹,

Marsano²,

Papadodimas³

et al. 2008

We geometrically engineer N = 2 theories perturbed by a superpotential by adding 3-form flux with support at infinity to local Calabi-Yau geometries in type IIB. This allows us to apply the formalism of Ooguri, Ookouchi, and Park [arXiv:0704.3613] to demonstrate that, by tuning the flux at infinity, we can stabilize the dynamical complex structure moduli in a metastable, supersymmetry-breaking configuration. Moreover, we argue that this setup can arise naturally as a limit of a larger Calabi-Yau which separates into two weakly interacting regions; the flux in one region leaks into the other, where it appears to be supported at infinity and induces the desired superpotential. In our endeavor to confirm this picture in cases with many 3-cycles, we also compute the CIV-DV prepotential for arbitrary number of cuts up to fifth order in the glueball fields.

“…At each point of the moduli space, the low energy theory is described by an N = 2 effective theory where the gauge group is broken to U(1) Nc−1 . All the information about hte N = 2 theory is encoded in a particular meromorphic one-form dλ SW defined over an auxiliary curve, the Seiberg-Witten curve [22,35] …”

Section: Exact Superpotentials For Su(n C ) Theories In Confining Vacuamentioning

confidence: 99%

Exact Superpotentials, Theories with Flavor and Confining Vacua

Gómez–Reino

2004

In this paper we study some interesting properties of the effective superpotential of N = 1 supersymmetric gauge theories with fundamental matter, with the help of the Dijkgraaf-Vafa proposal connecting supersymmetric gauge theories with matrix models. We find that the effective superpotential for theories with N f fundamental flavors can be calculated in terms of quantities computed in the pure (N f = 0) gauge theory. Using this property we compute in a remarkably simple way the exact effective superpotential of N = 1 supersymmetric theories with fundamental matter and gauge group SU(N c ), at the point in the moduli space where a maximal number of monopoles become massless (confining vacua). We extend the analysis to a generic point of the moduli space, and show how to compute the effective superpotential in this general case.