Complete prepotential for 5d $$ \mathcal{N} $$ = 1 superconformal field theories

Motivated by understanding M2-branes, we propose to reformulate partition functions of M2-branes by quantum curves. Especially, we focus on the backgrounds of del Pezzo geometries, which enjoy Weyl group symmetries of exceptional algebras. We construct quantum curves explicitly and turn to the analysis of classical phase space areas and quantum mirror maps. We find that the group structure helps in clarifying previous subtleties, such as the shift of the chemical potential in the area and the identification of the overall factor of the spectral operator in the mirror map. We list the multiplicities characterizing the quantum mirror maps and find that the decoupling relation known for the BPS indices works for the mirror maps. As a result, with the group structure we can present explicitly the statement for the correspondence between spectral theories and topological strings on del Pezzo geometries.

Section: Jhep10(2020)154supporting

confidence: 64%

Spectral theories and topological strings on del Pezzo geometries

Moriyama

2020

“…Recently, the complete prepotential of certain five-dimensional low rank gauge theories was proposed which is valid in the entire region of parameter space [35]. It would be interesting to extend the complete prepotential to arbitrarily high rank theories and compare this with the localization results described in this paper.…”

Section: Discussion and Outlookmentioning

confidence: 79%

Five-dimensional gauge theories on spheres with negative couplings

Minahan

Nedelin

2021

We consider supersymmetric gauge theories on S5 with a negative Yang-Mills coupling in their large N limits. Using localization we compute the partition functions and show that the pure SU(N) gauge theory descends to an SU(N/2)+N/2× SU(N/2)−N/2× SU(2) Chern-Simons gauge theory as the inverse ’t Hooft coupling is taken to negative infinity for N even. The Yang-Mills coupling of the SU(N/2)±N/2 is positive and infinite, while that on the SU(2) goes to zero. We also show that the odd N case has somewhat different behavior. We then study the SU(N/2)N/2 pure Chern-Simons theory. While the eigenvalue density is only found numerically, we show that its width equals 1 in units of the inverse sphere radius, which allows us to find the leading correction to the free energy when turning on the Yang-Mills term. We then consider USp(2N) theories with an antisymmetric hypermultiplet and Nf< 8 fundamental hypermultiplets and carry out a similar analysis. Along the way we show that the one-instanton contribution to the partition function remains exponentially suppressed at negative coupling for the SU(N) theories in the large N limit.

“…One advantage of these brane constructions is that they capture the dynamics of the corresponding 5d gauge theories and, simultaneously, their UV fixed points. Recent developments using brane webs include [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. As known from the SU (2) example with N f < 8 flavours [1,2], it is important to understand the enhancement of the global symmetry of these theories at the fixed point.…”

Section: Introductionmentioning

confidence: 99%

Magnetic quivers from brane webs with O5 planes

Bourget

Grimminger

Hanany

et al. 2020

145

Magnetic quivers have led to significant progress in the understanding of gauge theories with 8 supercharges at UV fixed points. For a given low-energy gauge theory realised via a Type II brane construction, there exist magnetic quivers for the Higgs branches at finite and infinite gauge coupling. Comparing these moduli spaces allows one to study the non-perturbative effects when transitioning to the fixed point. For 5d N = 1 SQCD, 5-brane webs have been an important tool for deriving magnetic quivers. In this work, the emphasis is placed on 5-brane webs with orientifold 5-planes which give rise to 5d theories with orthogonal or symplectic gauge groups. For this setup , the magnetic quiver prescription is derived and contrasted against a unitary magnetic quiver description extracted from an O7 − construction. Further validation is achieved by a derivation of the associated Hasse diagrams. An important class of families considered are the orthogonal exceptional E n families (−∞ < n ≤ 8), realised as infinite coupling Higgs branches of Sp(k) gauge theories with fundamental matter. In particular, the moduli spaces are realised by a novel type of magnetic quivers, called unitary-orthosymplectic quivers.