Intersecting D3-branes and Holography

TL;DR

This work analyzes a defect CFT from intersecting D3-branes preserving (4,4) supersymmetry, presenting an exact Lagrangian description that combines 2d defect and 4d bulk degrees of freedom. In the holographic regime, a probe D3'-brane wraps an $AdS_3\times S^1$ subspace of $AdS_5\times S^5$, and a detailed AdS/CFT dictionary maps KK fluctuations to defect operators, including a holomorphic Higgs-branch curve $wy=c\alpha^{\prime}$ and a family of BPS primaries. A nonrenormalization conjecture is supported by both large-$\lambda$ (via AdS/CFT) and perturbative weak-coupling checks, suggesting protected correlators for a subset of defect operators. The analysis emphasizes the role of two-dimensional massless scalars on the defect, IR effects that spread the vacuum over the Higgs branch, and the need to sum over holomorphic embeddings in the holographic computation. Overall, the work advances understanding of defect holography, the structure of the 2d/4d coupled theory, and the prospects for nonrenormalization in impurity CFTs.

Abstract

We study a defect conformal field theory describing D3-branes intersecting over two space-time dimensions. This theory admits an exact Lagrangian description which includes both two- and four-dimensional degrees of freedom, has (4,4) supersymmetry and is invariant under global conformal transformations. Both two- and four-dimensional contributions to the action are conveniently obtained in a two-dimensional (2,2) superspace. In a suitable limit, the theory has a dual description in terms of a probe D3-brane wrapping an AdS_3 x S^1 slice of AdS_5 x S^5. We consider the AdS/CFT dictionary for this set-up. In particular we find classical probe fluctuations corresponding to the holomorphic curve wy=cα^{\prime}. These fluctuations are dual to defect fields containing massless two-dimensional scalars which parameterize the classical Higgs branch, but do not correspond to states in the Hilbert space of the CFT. We also identify probe fluctuations which are dual to BPS superconformal primary operators and to their descendants. A non-renormalization theorem is conjectured for the correlators of these operators, and verified to order g^2.

Figures (5)

• Figure 1: Holomorphic curve $wy=cL^2$.
• Figure 2: AdS/CFT duality for an Impurity CFT. The duality acts twice. Once for the IIB supergravity on $AdS_5 \times S^5$, and once for DBI theory on $AdS_3 \times S^1$.
• Figure 3: Decomposition of the two $SU(4)$ R-symmetries.
• Figure 4: One of the four graphs of the correlator $\langle {\cal C}^l(x) \bar{\cal C}^l(y) \rangle$.
• Figure 5: First order corrections to the correlator $\langle {\cal C}^l(x) \bar{\cal C}^l(y) \rangle$ for $l=0$.