Janus interface entropy and Calabi’s diastasis in four-dimensional $$ \mathcal{N} $$ = 2 superconformal field theories

Self Cite

We describe conformal defects of p dimensions in a free scalar theory on a d-dimensional flat space as boundary conditions on the conformally flat space ℍp+1× 𝕊d−p−1. We classify two types of boundary conditions, Dirichlet type and Neumann type, on the boundary of the subspace ℍp+1 which correspond to the types of conformal defects in the free scalar theory. We find Dirichlet boundary conditions always exist while Neumann boundary conditions are allowed only for defects of lower codimensions. Our results match with a recent classification of the non-monodromy defects, showing Neumann boundary conditions are associated with non-trivial defects. We check this observation by calculating the difference of the free energies on ℍp+1× 𝕊d−p−1 between Dirichlet and Neumann boundary conditions. We also examine the defect RG flows from Neumann to Dirichlet boundary conditions and provide more support for a conjectured C-theorem in defect CFTs.

Section: Jhep05(2021)074mentioning

confidence: 99%

Free energy and defect C-theorem in free scalar theory

Nishioka

Sato

2021

Self Cite

“…The same map was applied to the interface entropy to derive a universal relation between the entropy and sphere free energy [41,46], but there is a crucial difference between the pseudo entropy and interface entropy as the number of the interfaces between the two…”

Section: Jhep09(2021)015mentioning

confidence: 99%

Topological pseudo entropy

Nishioka

Takayanagi

Taki

2021

Self Cite

We introduce a pseudo entropy extension of topological entanglement entropy called topological pseudo entropy. Various examples of the topological pseudo entropies are examined in three-dimensional Chern-Simons gauge theory with Wilson loop insertions. Partition functions with knotted Wilson loops are directly related to topological pseudo (Rényi) entropies. We also show that the pseudo entropy in a certain setup is equivalent to the interface entropy in two-dimensional conformal field theories (CFTs), and leverage the equivalence to calculate the pseudo entropies in particular examples. Furthermore, we define a pseudo entropy extension of the left-right entanglement entropy in two-dimensional boundary CFTs and derive a universal formula for a pair of arbitrary boundary states. As a byproduct, we find that the topological interface entropy for rational CFTs has a contribution identical to the topological entanglement entropy on a torus.

“…Earlier general considerations for the case with boundaries can be found in [17,60,61]. More recent results involving localization and supersymmetric boundaries and interfaces include [31,42,62,63].…”

Section: Localization Calculationmentioning

confidence: 99%

“…Similar calculations were performed in[29] for 3D superconformal theories and in[30] for 3D BCFTs 4. Localization calculations of F for related 3D SCFTs were performed in[29], and calculations of the interface entropy for supersymmetric Janus interfaces in 4D N = 2 SCFTs were performed in[31].…”

mentioning

confidence: 99%

Holographic and localization calculations of boundary F for $$ \mathcal{N} $$ = 4 SUSY Yang-Mills theory

Raamsdonk

Waddell

2021

$$ \mathcal{N} $$ N = 4 Supersymmetric Yang-Mills (SYM) theory can be defined on a half-space with a variety of boundary conditions preserving scale invariance and half of the original supersymmetry; more general theories with the same symmetry can be obtained by coupling to a 3D SCFT at the boundary. Each of these theories is characterized by a quantity called “boundary F”, conjectured to decrease under boundary renormalization group flows. In this paper, we calculate boundary F for U(N) $$ \mathcal{N} $$ N = 4 SYM theory with the most general half-supersymmetric boundary conditions arising from string theory constructions with D3-branes ending on collections of D5-branes and/or NS5-branes. We first perform the calculation holographically by evaluating the entanglement entropy for a half-ball centered on the boundary using the Ryu-Takayanagi formula in the dual type IIB supergravity solutions. For boundary conditions associated with D3-branes ending on D5 branes only or NS5-branes only, we also calculate boundary F exactly by evaluating the hemisphere partition function using supersymmetric localization. The leading terms at large N in the supergravity and localization results agree exactly as a function of the t’ Hooft coupling λ.