D-branes in AdS_3xS^3xS^3xS^1

TL;DR

The paper analyzes D-branes in $AdS_3\times S^3\times S^3\times S^1$ with NS-NS flux using boundary-state techniques. It identifies two classes of conformally invariant gluing conditions, $R_I$ (inner) and $R_{II}$ (outer), yielding branes built from shifted conjugacy classes and twisted conjugacy classes in $SU(2)\times SU(2)$, respectively; $R_{II}$ exists when $k_2=k_3$. It shows twisted conjugacy classes in $SU(2)\times SU(2)$ are inverse images of ordinary $SU(2)$ conjugacy classes, giving $S^3$ and $S^2\times S^3$-type worldvolumes, and proves that all bosonic configurations admit an $N=1$ supersymmetric extension. Spacetime supersymmetry analysis reveals that many D-branes preserve half of the spacetime SUSY (BPS), including several $R_I$- and $R_{II}$-type configurations, with a detailed fermionic boundary-state treatment supporting these results. The work extends known AdS$_3$ backgrounds by revealing a richer D-brane spectrum mediated by twisted conjugacy and automorphism structure, with implications for brane dynamics and holography in this geometry.

Abstract

We analyse the possible D-brane configurations in an AdS_3xS^3xS^3xS^1 background with a NS-NS B field, by using the boundary state formalism. We study their geometry and we determine the fraction of spacetime supersymmetry preserved by these solutions.

Theorems & Definitions (5)

• Theorem 1
• proof
• Theorem 2
• Theorem 3
• Theorem 4