Two-dimensional SCFTs from wrapped branes and c-extremization

Abstract: We apply c-extremization, whose proof we review in full detail, to study two-dimensional N=(0,2) superconformal field theories arising from the low-energy dynamics of D3-branes wrapped on Riemann surfaces and M5-branes wrapped on four-manifolds. We compute the exact central charges of these theories using anomalies and c-extremization. In all cases we also construct AdS_3 supergravity solutions of type IIB and eleven-dimensional supergravity, which are holographic duals to the field theories at large N, and exactly reproduce the central charges computed via c-extremization.

• The paper computes exact central charges of 2D SCFTs emerging from wrapped branes using the c-extremization method.
• It validates field theory predictions by matching anomaly evaluations with AdS3 supergravity duals in type IIB and eleven-dimensional frameworks.
• It extends twisted compactification analyses of 4D N=4 SYM and 6D N=(2,0) theories, providing a systematic framework for holographic SCFT studies.

Two-dimensional SCFTs from wrapped branes and $c$-extremization

The paper by Francesco Benini and Nikolay Bobev provides an in-depth exploration into the field of two-dimensional $N=(0,2)$ superconformal field theories (SCFTs) that emerge from the low-energy dynamics of D3-branes wrapped on Riemann surfaces and M5-branes wrapped on four-manifolds. A crucial aspect of this work is the application of the $c$-extremization principle, a technique introduced by the authors in previous work, which enables the precise determination of the superconformal R-symmetry in these theories.

The primary aim of the paper is to calculate the exact central charges for these SCFTs, which are pivotal quantities characterizing the conformal properties. The approach hinges on evaluating anomalies and employing $c$-extremization. The authors achieve a methodical calculation of central charges and further substantiate their findings by constructing corresponding AdS$_3$ supergravity solutions. These solutions, framed within the contexts of type IIB and eleven-dimensional supergravity, serve as holographical duals to the field theories at large $N$. The consistency between the central charges derived from field theory and those computed holographically underscores the validity of their methods.

The paper details two distinct types of SCFTs derived from the compactification processes. The first class pertains to twisted compactifications of four-dimensional $N=4$ super-Yang-Mills theory on Riemann surfaces, a framework originally analyzed by Bershadsky et al. and Maldacena et al. The authors extend this work by utilizing $c$-extremization to accurately pinpoint the IR R-symmetry and central charges. Notably, in instances where large $N$ solutions of type IIB supergravity were previously known, Benini and Bobev confirm that these agree with field theory predictions obtained via $c$-extremization.

A second pivotal focus is the compactification of the six-dimensional $N=(2,0)$ theory on products of closed Riemann surfaces. Here, the analysis extends to a wider spectrum, considering various types of four-manifolds. Such treatments include Kähler four-cycles in Calabi-Yau fourfolds, special Lagrangian four-cycles in hyper-Kähler fourfolds, among others. The authors derive new solutions in supergravity, uncovering intricate relationships between geometry and the field theories in question. Again, the holographic computations align with those inferred from $c$-extremization, highlighting the robustness of their methodology.

The work is comprehensive, addressing diverse aspects such as potential anomalies, complex flavor dynamics, and gravitational contributions. Despite the complexity of the models examined, the authors manage to showcase how intricate calculations can be streamlined through $c$-extremization, thereby facilitating new insights into SCFTs and their dual supergravity descriptions.

The ramifications of these explorations are significant both theoretically and practically. Theoretically, they lend credence to the principle of $c$-extremization, presenting it as a powerful tool for addressing difficult calculations in SCFTs without recourse to Lagrangian descriptions. Practically, these models, underpinning concrete string theory constructions, enrich our understanding of holography in lower-dimensional settings.

The paper further leaves room for speculative advancement. By providing a framework to systematically derive and validate SCFT characteristics, it opens avenues for future work, particularly in extending $c$-extremization to broader contexts or identifying new holographic correspondences. The examples discussed may serve as templates for exploring novel two-dimensional quantum field theories, with implications that could stretch across both mathematical and theoretical physics domains.

In summary, Benini and Bobev contribute a significant piece to the ongoing dialogue concerning wrapped branes and their associated field theories. Their thorough calculations and holographic corroborations lay a foundation for continued exploration into the intersecting worlds of geometry, field theory, and string dynamics, with $c$-extremization at its core.