Mirror symmetry and line operators

101

For a single free scalar field in d ≥ 2 dimensions, almost all the unitary conformal defects must be ‘trivial’ in the sense that they cannot hold interesting dynamics. The only possible exceptions are monodromy defects in d ≥ 4 and co-dimension three defects in d ≥ 5. As an intermediate result we show that the n-point correlation functions of a conformal theory with a generalized free spectrum must be those of the generalized free theory.

Section: Applicationssupporting

confidence: 92%

Line and surface defects for the free scalar field

Lauria

Liendo

Rees

et al. 2021

101

“…where W −k is a Wilson line of charge −k ending on the boundary, which admits boundary operators of gauge charge k. In a similar manner to the line operators in the bulk theory [28,29], the Wilson and vortex lines are swapped under mirror symmetry. We also discuss that the H-twist and C-twist limits [3,11] of the half-indices lead to the reduced indices which count the boundary operators corresponding to the modules which arise from the N = (2, 2) half-BPS boundary conditions for the quantized Coulomb and Higgs branch algebras.…”

Section: Jhep03(2021)163mentioning

confidence: 99%

Abelian mirror symmetry of $$ \mathcal{N} $$ = (2, 2) boundary conditions

Okazaki

2021

We evaluate half-indices of $$ \mathcal{N} $$ N = (2, 2) half-BPS boundary conditions in 3d $$ \mathcal{N} $$ N = 4 supersymmetric Abelian gauge theories. We confirm that the Neumann boundary condition is dual to the generic Dirichlet boundary condition for its mirror theory as the half-indices perfectly match with each other. We find that a naive mirror symmetry between the exceptional Dirichlet boundary conditions defining the Verma modules of the quantum Coulomb and Higgs branch algebras does not always hold. The triangular matrix obtained from the elliptic stable envelope describes the precise mirror transformation of a collection of half-indices for the exceptional Dirichlet boundary conditions.

“…Another important potential modification involves half-BPS line defects placed along the 1d locus in the boundary/interface. These modify directly A H or A C [74], depending on the type of line defect. Topological correlators supported on Wilson lines of the bulk 2d cYM, in the electric case, were also explored in [75][76][77].…”

Section: Special Features Of the A Hmentioning

confidence: 99%

“…We could also include boundary line defects modifying A C [74], circular Wilson and 't Hooft loops linking the (x 3 , x 4 ) plane resulting in different traces on A C , and could also study surface operators in the cohomology. Our focus is on local operators supported on boundaries and interfaces only.…”

Section: Jhep12(2021)050mentioning

confidence: 99%

Algebras, traces, and boundary correlators in $$ \mathcal{N} $$ = 4 SYM

Dedushenko

Gaiotto

2021

We study supersymmetric sectors at half-BPS boundaries and interfaces in the 4d $$ \mathcal{N} $$ 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 $$ U\left(\mathfrak{g}\right) $$ U g with the trace describing the Dirichlet boundary conditions; and the finite W-algebra $$ \mathcal{W}\left(\mathfrak{g},{t}_{+}\right) $$ W g t + with the trace describing the Nahm pole boundary conditions.