Abstract
In this paper, we study 5d mathcal{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-type singularities.
Highlights
Introduction and main resultsSupersymmetric gauge theory has rich structures and applications in the study of nonperturbative quantum field theories
This correspondence indicates that the topological vertex formalism can be reinterpreted as the method to compute partition function for a given 5-brane web diagram
5-brane intersect with the O5-plane as given in the right half of figure 9. Since these two different phases are realized in different parameter regions of an identical gauge theory, the partition function should be invariant under this phase transition, analogous to the flop invariance of the topological string partition function [44, 45]
Summary
Supersymmetric gauge theory has rich structures and applications in the study of nonperturbative quantum field theories. We consider 5d N = 1 Sp(N ) gauge theories with Nf flavors and discuss its relation with Seiberg-Witten theory based on 5-brane web diagram with O5-plane. We construct the Seiberg-Witten curve for 5d N = 1 Sp(N ) gauge theory with Nf flavors from the 5-brane web diagram with O5-plane by generalizing the computation in [19]. This class of theories are expected to have UV fixed point for. T+ (w) and t− (w) exchange with each other under the transformation w → w−1
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
