S-duality wall of SQCD from Toda braiding
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Springer
Received: August 21, 2020 Accepted: September 22, 2020 Published: October 23, 2020
B. Le Floch Princeton Center for Theoretical Science, Princeton University, Princeton, NJ 08544, U.S.A. ´ Philippe Meyer Institute, Physics Department, Ecole Normale Sup´erieure, PSL Research University, 24 rue Lhomond, F-75231 Paris Cedex 05, France
E-mail: [email protected] Abstract: Exact field theory dualities can be implemented by duality domain walls such that passing any operator through the interface maps it to the dual operator. This paper describes the S-duality wall of four-dimensional N = 2 SU(N ) SQCD with 2N hypermultiplets in terms of fields on the defect, namely three-dimensional N = 2 SQCD with gauge group U(N − 1) and 2N flavours, with a monopole superpotential. The theory is self-dual under a duality found by Benini, Benvenuti and Pasquetti, in the same way that T [SU(N )] (the S-duality wall of N = 4 super Yang-Mills) is self-mirror. The domain-wall theory can also be realized as a limit of a USp(2N − 2) gauge theory; it reduces to known results for N = 2. The theory is found through the AGT correspondence by determining the braiding kernel of two semi-degenerate vertex operators in Toda CFT. Keywords: Supersymmetry and Duality, Conformal and W Symmetry, Duality in Gauge Field Theories, Supersymmetric Gauge Theory ArXiv ePrint: 1512.09128
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)152
JHEP10(2020)152
S-duality wall of SQCD from Toda braiding
Contents 1 Introduction
1
2 AGT relation 2.1 Localization 2.2 Toda CFT 2.3 Special functions
4 4 6 8 9 10 11 12 14 15
4 Braiding kernel 4.1 Main formula 4.2 Reduction to fully degenerate 4.3 Shift relation from pentagon identity
19 19 21 23
5 Domain wall and its symmetries 5.1 Continuous flavour symmetries 5.2 Partition function 5.2.1 U(N − 1) description 5.2.2 USp(2N − 2) description 5.3 Discrete symmetries and dualities
26 26 29 29 31 32
6 Conclusions
35
1
Introduction
Extended operators, such as Wilson and ’t Hooft loops [1, 2], surface operators [3–5], and domain walls [6–8] can serve as order parameters [1, 2, 9] and help probe dualities of gauge theories. Exact all-scale dualities such as S-duality map all correlators of one theory to the dual theory through some dictionary that must be worked out on a case by case basis. For instance, S-duality of four-dimensional N = 2 supersymmetric gauge theories [10, 11] interchanges Wilson (electric) and ’t Hooft (magnetic) loop operators [12–15], as befitting of this generalization of electric-magnetic duality. Given an exact duality between theories T1 and T2 , what happens if one dualizes one half-space, say y ≥ 0? Start with T1 on all of space. After dualizing, the system should be described by T1 for y < 0 and T2 for y > 0, separated by a codimension 1 interface (wall) at
–1–
JHEP10(2020)152
3 Braiding matrices 3.1 Braiding a fundamental degenerate 3.1.1 Monodromy matrices 3.1.2 Explicit conformal blocks (proof) 3.1.3 Braiding matrices 3.2 Bra
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