Aspects of AdS/BCFT (1108.5152v2)

Abstract: We expand the results of arXiv:1105.5165, where a holographic description of a conformal field theory defined on a manifold with boundaries (so called BCFT) was proposed, based on AdS/CFT. We construct gravity duals of conformal field theories on strips, balls and also time-dependent boundaries. We show a holographic g-theorem in any dimension. As a special example, we can define a `boundary central charge' in three dimensional conformal field theories and our holographic g-theorem argues that it decreases under RG flows. We also computed holographic one-point functions and confirmed that their scaling property agrees with field theory calculations. Finally, we give an example of string theory embedding of this holography by inserting orientifold 8-planes in AdS(4)xCP(3).

• The paper introduces novel holographic duals for BCFTs defined on varied geometries and extends the g-theorem to higher dimensions.
• It employs meticulous holographic one-point function derivations that confirm the interplay of bulk and boundary effects in BCFTs.
• The work integrates string theory embeddings to address gauge anomalies and offer concrete models for boundary dynamics.

An Overview of "Aspects of AdS/BCFT"

The paper "Aspects of AdS/BCFT" by Fujita, Takayanagi, and Tonni extends the framework of the AdS/CFT correspondence to boundary conformal field theories (BCFTs), which are conformal field theories (CFTs) defined on manifolds with boundaries. This work investigates a holographic description of BCFTs by introducing a new geometry that includes both the usual asymptotic AdS boundary and an additional boundary to account for the effects of the physical boundary in the CFT. The paper covers mathematical formulations, holographic techniques, and theoretical implications that arise from this setup.

The central results of the paper are organized into different sections, each illuminating aspects of the AdS/BCFT correspondence. Key highlights include:

Holographic Duals for Various Geometries

The authors construct gravity duals for BCFTs defined on different geometries such as strips, balls, and time-dependent boundaries. These constructions extend the primary framework of AdS/CFT by incorporating boundary conditions that reflect the BCFTs' characteristics. In doing so, the concept of a holographic g-theorem is introduced for any dimension, signifying that the boundary central charge decreases along the renormalization group (RG) flows, an assertion supported by holographic one-point function calculations.

Holographic g-Theorem

The holographic g-theorem extends the c-theorem, which asserts the decrease of the central charge in two-dimensional CFT under RG flows, to higher dimensions and BCFTs. The g-function, representing the boundary entropy, is shown to decrease under RG flows, reflecting the decrement of degrees of freedom as the system evolves. This finding is crucial because it generalizes the understanding of RG flows in the presence of boundaries, supported by the null energy condition imposed.

One-Point Function and Conformal Boundary Theories

Through a meticulous derivation, the paper computes holographic one-point functions. The presence of boundary-induced terms alters these functions, which aligns well with predictions from conformal field theory, thereby affirming the robustness of the holographic approach. The scaling behavior of these functions remains consistent across the usual and boundary-modified settings, highlighting the interplay between bulk and boundary effects.

String Theory Embedding

The paper demonstrates a string theory embedding of AdS/BCFT through the construction based on type IIA string theory on AdS$_4 \times$ CP$^3$, involving orientifold planes and D-branes. This provides a concrete holographic representation of a BCFT, supported by gauge anomaly cancellation via the presence of chiral fermions localized at boundaries. This adds a practical dimension to the theoretical modeling of BCFTs and offers pathways for further research into the interplay between bulk and boundary theories in string theory.

Implications and Future Directions

The implications of this research extend both practically, in terms of constructing realistic models of physical systems with boundaries, and theoretically in exploring deeper aspects of non-perturbative phenomena. The work implicitly challenges the community to further explore holographic setups incorporating more complicated boundary geometries and topologies, thereby enriching the scope of holography in describing real-world systems. Future developments may also focus on computational techniques for extending these models to non-trivial bulk dynamics and understanding the impact of these setups on boundary dynamics.

This work represents a significant advancement in understanding the holographic correspondence in theories with boundaries, opening potential for novel insights into field theories and gravity.