5-brane webs for 5d N=1 G_2 gauge theories

Physics Letters B, 2001

We present string duals of four dimensional N = 2 pure SU(N) SYM theory. The theory is obtained as the low energy limit of D5-branes wrapped on non-trivial two-cycles. Using seven dimensional gauged supergravity and uplifting the result to ten dimensions, we obtain solutions corresponding to various points of the N = 2 moduli space. The more symmetric solution may correspond to a point with rotationally invariant classical vevs. By turning on seven dimensional scalar fields, we find a solution corresponding to a linear distribution of vevs. Both solutions are conveniently studied with a D5-probe, which also confirms many of the standard expectations for N = 2 solutions.

Journal of High Energy Physics, 2012

In this article we explore the duality between the low energy effective theory of fivedimensional N = 1 SU (N) M −1 and SU (M) N −1 linear quiver gauge theories compactified on S 1. The theories we study are the five-dimensional uplifts of four-dimensional superconformal linear quivers. We study this duality by comparing the Seiberg-Witten curves and the Nekrasov partition functions of the two dual theories. The Seiberg-Witten curves are obtained by minimizing the worldvolume of an M5-brane with nontrivial geometry. Nekrasov partition functions are computed using topological string theory. The result of our study is a map between the gauge theory parameters, i.e., Coulomb moduli, masses and UV coupling constants, of the two dual theories. Apart from the obvious physical interest, this duality also leads to compelling mathematical identities. Through the AGTW conjecture these five-dimentional gauge theories are related to q-deformed Liouville and Toda SCFTs in two-dimensions. The duality we study implies the relations between Liouville and Toda correlation functions through the map we derive.

Journal of High Energy Physics, 2021

In this paper, we study 5d $$ \mathcal{N} $$ N = 1 Sp(N) gauge theory with Nf (≤ 2N + 3) flavors based on 5-brane web diagram with O5-plane. On the one hand, we discuss Seiberg-Witten curve based on the dual graph of the 5-brane web with O5-plane. On the other hand, we compute the Nekrasov partition function based on the topological vertex formalism with O5-plane. Rewriting it in terms of profile functions, we obtain the saddle point equation for the profile function after taking thermodynamic limit. By introducing the resolvent, we derive the Seiberg-Witten curve and its boundary conditions as well as its relation to the prepotential in terms of the cycle integrals. They coincide with those directly obtained from the dual graph of the 5-brane web with O5-plane. This agreement gives further evidence for mirror symmetry which relates Nekrasov partition function with Seiberg-Witten curve in the case with orientifold plane and shed light on the non-toric Calabi-Yau 3-folds including D-...

Journal of High Energy Physics

We study the Higgs branch of 5d superconformal theories engineered from brane webs with orientifold five-planes. We propose a generalization of the rules to derive magnetic quivers from brane webs pioneered in [1], by analyzing theories that can be described with a brane web with and without O5 planes. Our proposed magnetic quivers include novel features, such as hypermultiplets transforming in the fundamental-fundamental representation of two gauge nodes, antisymmetric matter, and ℤ2 gauge nodes. We test our results by computing the Coulomb and Higgs branch Hilbert series of the magnetic quivers obtained from the two distinct constructions and find agreement in all cases.

Physical Review D, 2006

We study the dimensional reduction of M5-branes wrapping special Lagrangian 3-cycles of a Calabi-Yau manifold and show explicitly that they result in 2-branes coupled to the hypermultiplets of ungauged N=2 D=5 supergravity theory. In addition to confirming previously known results, the calculation proves the relationship between them and provides further insight on how the topological properties of the compact space affect the lower dimensional fields.

Physical Review D, 2019

In previous works [J. High Energy Phys. 07 (2017) 112; Phys. Rev. D 97, 046004 (2018); J. High Energy Phys. 11 (2018) 016], we studied a class of toric Calabi-Yau threefolds which engineer six-dimensional supersymmetric gauge theories with gauge group UðNÞ and adjoint matter. The Kähler moduli space of these manifolds can be extended through flop transformations to include regions which are described by so-called shifted toric web diagrams. In this paper, we analyze gauge theories that are engineered by these shifted toric web diagrams and argue that, in specific limits, some of them engineer five-dimensional quiver gauge theories with gauge group G ⊂ UðNÞ and with fundamental and bifundamental matter. We discuss several examples in detail and describe how the matter sector is obtained from the six-dimensional parent theory.

2016

We discussed a one-point function of a BPS Wilson loop in a supersymmetric five dimensional gauge theories defined on M 4 ×S 1 by using path integral expression of Wilson loops. We found that the Wilson loop gives interaction terms between charged particles and certain gauge fields on the instanton moduli space, and makes the non-charged particle charged under the gauge fields.

Journal of High Energy Physics, 2019

We propose 5d descriptions of 6d $$ \mathcal{N}=\left(1,\ 0\right) $$ N = 1 , 0 superconformal field theories arising from Type IIA brane configurations with an O8−-plane. We T-dualize the brane diagram along a compactification circle and obtain a 5-brane web diagram with two O7−- planes. The gauge theory description of the resulting 5d theory for a given 6d superconformal field theory is not unique, and we argue that the non-uniqueness leads to various dual 5d gauge theories. There are three sources which lead to the 5d dualities. One type comes from either resolving both or one of the two O7−-planes. The two situations give us two different ways to read off a 5d gauge theory from essentially the same web diagram. The second type originates from different distributions of D5 or D7-branes, shifting the gauge group ranks of the 5d quiver theory. The last one comes from the 90 or 45 degree rotations of the 5-brane web diagram, which is a part of the SL(2, ℤ) duality of Type IIB string...

Moscow Mathematical Journal

We study supersymmetric gauge theories in five dimensions, using their relation to the K-theory of the moduli spaces of torsion free sheaves. In the spirit of the BPS/CFT correspondence the partition function and the expectation values of the chiral, BPS protected observables are given by the matrix elements and more generally by the correlation functions in some q-deformed conformal field theory in two dimensions. We show that the coupling of the gauge theory to the bi-fundamental matter hypermultiplet inserts a particular vertex operator in this theory. In this way we get a generalization of the main result of \\cite{CO} to $K$-theory. The theory of interpolating Macdonald polynomials is an important tool in our construction.

2011

We revisit the relation of the six-dimensional (2, 0) M5-brane Conformal Field Theory compactified on S 1 to 5D maximally supersymmetric Yang-Mills Gauge Theory. We show that in the broken phase 5D super-Yang-Mills contains a spectrum of soliton states that can be identified with the complete Kaluza-Klein modes of an M2-brane ending on the M5-branes. This provides evidence that the (2, 0) theory on S 1 is equivalent to 5D super-Yang-Mills with no additional UV degrees of freedom, suggesting that the latter is in fact a well-defined quantum theory and possibly finite.