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Half-BPS Solutions locally asymptotic to AdS_3 x S^3 and interface conformal field theories

Marco Chiodaroli, Michael Gutperle, Darya Krym

TL;DR

This work constructs and analyzes half-BPS solutions of Type IIB supergravity that are locally asymptotic to $AdS_3\times S^3$ and are dual to interface CFTs in the D1-D5 system. The local solutions are fully determined by two holomorphic functions $A,B$ and two harmonic functions $\hat h,H$, with the bosonic fields obtained explicitly from this data. Regularity constraints yield Janus-type backgrounds with two AdS$_3$ regions and, more generally, multi-pole configurations with $n$ regions; the RR and NS-NS Janus solutions illustrate back-reacted interfaces with controlled charges. The holographic interpretation links massless bulk modes to marginal/interface operators $O_0$ and $T_0$ in the ${\cal N}=(4,4)$ 2D CFT, offering a concrete framework to study conformal defects and their counterterms in AdS$_3$/CFT$_2$.

Abstract

Type IIB superstring theory has AdS_3 x S^3 x M_4 (where the manifold M_4 is either K_3 or T^4) solutions which preserve sixteen supersymmetries. In this paper we consider half-BPS solutions which are locally asymptotic to AdS_3 x S^3 x M_4 and preserve eight of the sixteen supersymmetries. We reduce the BPS equations and the Bianchi identity for the self-dual five-form field to a set of four differential equations. The complete local solution can be parameterized in terms of two harmonic and two holomorphic functions and all bosonic fields have explicit expressions in terms of these functions. We analyze the conditions for global regularity and construct new half-BPS Janus-solutions which have two asymptotic AdS_3 regions. In addition, our analysis proves the global regularity of a class of solutions with more than two asymptotic AdS_3 regions. Finally, we discuss the dual interpretation as a supersymmetric interface theory for the half-BPS Janus solutions carrying only Ramond-Ramond three-form charge.

Half-BPS Solutions locally asymptotic to AdS_3 x S^3 and interface conformal field theories

TL;DR

This work constructs and analyzes half-BPS solutions of Type IIB supergravity that are locally asymptotic to and are dual to interface CFTs in the D1-D5 system. The local solutions are fully determined by two holomorphic functions and two harmonic functions , with the bosonic fields obtained explicitly from this data. Regularity constraints yield Janus-type backgrounds with two AdS regions and, more generally, multi-pole configurations with regions; the RR and NS-NS Janus solutions illustrate back-reacted interfaces with controlled charges. The holographic interpretation links massless bulk modes to marginal/interface operators and in the 2D CFT, offering a concrete framework to study conformal defects and their counterterms in AdS/CFT.

Abstract

Type IIB superstring theory has AdS_3 x S^3 x M_4 (where the manifold M_4 is either K_3 or T^4) solutions which preserve sixteen supersymmetries. In this paper we consider half-BPS solutions which are locally asymptotic to AdS_3 x S^3 x M_4 and preserve eight of the sixteen supersymmetries. We reduce the BPS equations and the Bianchi identity for the self-dual five-form field to a set of four differential equations. The complete local solution can be parameterized in terms of two harmonic and two holomorphic functions and all bosonic fields have explicit expressions in terms of these functions. We analyze the conditions for global regularity and construct new half-BPS Janus-solutions which have two asymptotic AdS_3 regions. In addition, our analysis proves the global regularity of a class of solutions with more than two asymptotic AdS_3 regions. Finally, we discuss the dual interpretation as a supersymmetric interface theory for the half-BPS Janus solutions carrying only Ramond-Ramond three-form charge.

Paper Structure

This paper contains 46 sections, 215 equations, 6 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Ten-dimensional ansatz and reduction of BPS equations
  3. Brief review of IIB supergravity fields
  4. The ten-dimensional ansatz
  5. Reduction of the ten-dimensional spinor
  6. Reduction of the ten-dimensional BPS equations
  7. Dilatino equation
  8. Gravitino in $AdS_{2}$ direction
  9. Gravitino in $S^{2}$ direction
  10. Gravitino in $K_{3}$ direction
  11. Gravitino in $\Sigma$ direction
  12. $\tau$ matrix notation
  13. Reduction of BPS equations by discrete symmetries
  14. Discrete symmetries
  15. Vanishing of bilinear constraints
  16. ...and 31 more sections

Figures (6)

  • Figure 1: Change of coordinates mapping the strip into the upper half plane.
  • Figure 2: Dilaton and axion profiles for a Janus deformation with $\psi=1/2$ and $\theta=0$. The parameters $k$ and $L$ have been set to one.
  • Figure 3: Dilaton and axion profiles for a Janus deformation with $\psi=0$ and $\theta=1/2$. The parameters $k$ and $L$ have been set to one.
  • Figure 4: Metric factors for a Janus deformation with $\psi=\theta=1/2$, $L=k=1$ and $b=0$.
  • Figure 5: Dilaton and metric factor $f_3$ for a multi-pole Janus deformation. $H$ is singular for $x=0,1, \infty$ with unit residues while $A$ has poles in $x=0,-1,2$ with unit residues and in $x=1$ with residue $1/2$.
  • ...and 1 more figures