Abstract
We study supersymmetric sectors at half-BPS boundaries and interfaces in the 4d mathcal{N} = 4 super Yang-Mills with the gauge group G, which are described by associative algebras equipped with twisted traces. Such data are in one-to-one correspondence with an infinite set of defect correlation functions. We identify algebras and traces for known boundary conditions. Ward identities expressing the (twisted) periodicity of the trace highly constrain its structure, in many cases allowing for the complete solution. Our main examples in this paper are: the universal enveloping algebra Uleft(mathfrak{g}right) with the trace describing the Dirichlet boundary conditions; and the finite W-algebra mathcal{W}left(mathfrak{g},{t}_{+}right) with the trace describing the Nahm pole boundary conditions.
Highlights
Boundary observables play especially important role in Quantum Field Theory (QFT) due to their direct practical relevance
We study supersymmetric sectors at half-BPS boundaries and interfaces in the 4d N = 4 super Yang-Mills with the gauge group G, which are described by associative algebras equipped with twisted traces
We study aspects of boundary operators in the 4d N = 4 super YangMills (SYM) with gauge group G, subject to half-BPS boundary conditions
Summary
Boundary observables play especially important role in Quantum Field Theory (QFT) due to their direct practical relevance. A rich class of boundary conditions preserving 3d N = 4 SUSY, and often the full superconformal symmetry, are known in the literature [1,2,3] They are amenable to study via certain techniques originally developed for purely three-dimensional theories with the same amount of SUSY. In the purely 3d case, the construction based on superconformal symmetry was discovered first in [4, 5], motivated by the similar construction of the chiral algebra in [11], which we refer to as the “Q + S” type construction In this approach, the operators from AH or AC live on a chosen line in spacetime.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
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
