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Ten-dimensional supersymmetric Janus solutions

Eric D'Hoker, John Estes, Michael Gutperle

Abstract

The reduced field equations and BPS conditions are derived in Type IIB supergravity for configurations of the Janus type, characterized by an $AdS_4$-slicing of $AdS_5$, and various degrees of internal symmetry and supersymmetry. A generalization of the Janus solution, which includes a varying axion along with a varying dilaton, and has SO(6) internal symmetry, but completely broken supersymmetry, is obtained analytically in terms of elliptic functions. A supersymmetric solution with 4 conformal supersymmetries, SU(3) internal symmetry, a varying axion along with a varying dilaton, and non-trivial $B_{(2)}$ field, is derived analytically in terms of genus 3 hyper-elliptic integrals. This supersymmetric solution is the 10-dimensional Type IIB dual to the $\N=1$ interface super-Yang-Mills theory with SU(3) internal symmetry previously found in the literature.

Ten-dimensional supersymmetric Janus solutions

Abstract

The reduced field equations and BPS conditions are derived in Type IIB supergravity for configurations of the Janus type, characterized by an -slicing of , and various degrees of internal symmetry and supersymmetry. A generalization of the Janus solution, which includes a varying axion along with a varying dilaton, and has SO(6) internal symmetry, but completely broken supersymmetry, is obtained analytically in terms of elliptic functions. A supersymmetric solution with 4 conformal supersymmetries, SU(3) internal symmetry, a varying axion along with a varying dilaton, and non-trivial field, is derived analytically in terms of genus 3 hyper-elliptic integrals. This supersymmetric solution is the 10-dimensional Type IIB dual to the interface super-Yang-Mills theory with SU(3) internal symmetry previously found in the literature.

Paper Structure

This paper contains 41 sections, 151 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Type IIB supergravity
  3. The generalized non-supersymmetric Janus solution
  4. Analytical solution in terms of elliptic functions
  5. Structure of the AdS/CFT dual
  6. The absence of breathing modes
  7. Supersymmetric interface CFT
  8. The ten-dimensional Janus Ansatz
  9. Symmetries of the Ansatz
  10. Invariant Metrics and Frames on $CP_2$
  11. Invariant 2-forms on $CP_2$ and $S^5$
  12. The Ansatz for the metric
  13. The Ansatz for the antisymmetric tensor fields
  14. Transformation properties under $SL(2,{\bf R})$
  15. The Reduced Bianchi identities and Field Equations
  16. ...and 26 more sections

Figures (6)

  • Figure 1: Mapping geodesic segments under $SL(2,{\bf R})$ in the dilaton/axion upper half plane.
  • Figure 2: Sketch of the boundary geometry of the Janus solution in global and Poincare coordinates for the $AdS_4$ slices.
  • Figure 3: The potential $V(\psi)$ for $C_2^2/\rho^8 =.36$
  • Figure 4: (a) Value of $\mu_0$ as a function of $C_2^2/\rho^8$, (b) dilaton for three values of parameters
  • Figure 5: (a) $f_4$ for three values of parameters, (b) $f_1$ and $f_2$ for three values of parameters
  • ...and 1 more figures