Yuji Tachikawa

Black hole entropy in the presence of Chern-Simons terms

We derive a formula for the black hole entropy in theories with gravitational Chern–Simons terms, by generalizing Walds argument which uses the Noether charge. It correctly reproduces the entropy of three-dimensional black holes in the presence of the Chern–Simons term, which was previously obtained via indirect methods.

Central charges of = 2 superconformal field theories in four dimensions

We present a general method for computing the central charges a and c of = 2 superconformal field theories corresponding to singular points in the moduli space of = 2 gauge theories. Our method relates a and c to the U(1)R anomalies of the topologically twisted gauge theory. We evaluate these anomalies by studying the holomorphic dependence of the path integral measure on the moduli. We calculate a and c for superconformal points in a variety of gauge theories, including = 4 SU(N), = 2 pure SU(N) Yang-Mills, and USp(2N) with 1 massless antisymmetric and 4 massive fundamental hypermultiplets. In the latter case, we reproduce the conformal and flavor central charges previously calculated using the gravity duals of these gauge theories. For any SCFT in the class under consideration, we derive a previously conjectured expression for 2a−c in terms of the sum of the dimensions of operators parameterizing the Coulomb branch. Finally, we prove that the ratio a/c is bounded above by 5/4 and below by 1/2.

Supersymmetric Completion of an R2 Term in Five-Dimensional Supergravity

We analyze the structure of a particular higher derivative correction of five-dimensional ungauged and gauged supergravity with eight supercharges. Specifically, we determine all the purely bosonic terms which are connected by the supersymmetry transformation to the mixed gauge-gravitational Chern-Simons term, W ∧ tr R ∧ R. Our construction utilizes the superconformal formulation of supergravity. As an application, we determine the condition for the supersymmetric anti-de Sitter vacuum with this term. We check that it gives precisely the same condition as the a-maximization in four-dimensional superconformal field theory on the boundary, as predicted by the AdS/CFT correspondence.

Six-dimensional D(N) theory and four-dimensional SO-USp quivers

We realize four-dimensional = 2 superconformal quiver gauge theories with alternating SO and USp gauge groups as compactifications of the six-dimensional DN theory with defects. The construction can be used to analyze infinitely strongly-coupled limits and S-dualities of such gauge theories, resulting in a new class of isolated four-dimensional = 2 superconformal field theories with SO(2N)3 flavor symmetry.

Higher-Derivative Corrections to the Asymptotic Virasoro Symmetry of 4d Extremal Black Holes

We study the asymptotic Virasoro symmetry which acts on the near-horizon region of extremal four-dimensional black hole solutions of gravity theories with higher-derivative corrections, following the recently proposed Kerr/CFT correspondence. We demonstrate that its central charge correctly reproduces the entropy formula of Iyer-Wald, once the boundary terms in the symplectic structure are carefully chosen.

A holographic computation of the central charges of d = 4, = 2 SCFTs

We use the AdS/CFT correspondence to compute the central charges of the d = 4, = 2 superconformal field theories arising from N D3-branes at singularities in F-theory. These include the conformal theories with En global symmetries. We compute the central charges a and c related to the conformal anomaly, and also the central charges k associated to the global symmetry in these theories. All of these are related to the coefficients of Chern-Simons terms in the dual string theory on AdS5. Our computation is exact for all values of N, enabling several tests of the dualities recently proposed by Argyres and Seiberg for the E6 and E7 theories with N = 1.

N=2 gauge theories and degenerate fields of Toda theory

We discuss the correspondence between degenerate fields of the W{sub N} algebra and punctures of Gaiottos description of the Seiberg-Witten curve of N=2 superconformal gauge theories. Namely, we find that the type of degenerate fields of the W{sub N} algebra, with null states at level one, is classified by Young diagrams with N boxes, and that the singular behavior of the Seiberg-Witten curve near the puncture agrees with that of W{sub N} generators. We also find how to translate mass parameters of the gauge theory to the momenta of the Toda theory.

N=2 S-duality via Outer-automorphism Twists

Compactification of 6D theory of type G on a punctured Riemann surface has been effectively used to understand S-dualities of 4D theories. We can further introduce branch cuts on the Riemann surface across which the worldvolume fields are transformed by the discrete symmetries associated with those of the Dynkin diagram of type G. This allows us to generate more S-dualities, and in particular to reproduce a couple of S-dual pairs found previously by Argyres and Wittig.

Comments on charges and near-horizon data of black rings

We study how the charges of the black rings measured at the asymptotic infinity are encoded in the near-horizon metric and gauge potentials, independent of the detailed structure of the connecting region. Our analysis clarifies how different sets of four-dimensional charges can be assigned to a single five-dimensional object under the Kaluza-Klein reduction. Possible choices are related by the Witten effect on dyons and by a large gauge transformation in four and five dimensions, respectively.

Rigid limit in = 2 supergravity and weak-gravity conjecture

We analyze the coupled = 2 supergravity and Yang-Mills system using holomorphy, near the rigid limit where the former decouples from the latter. We find that there appears generically a new mass scale around gMpl where g is the gauge coupling constant and Mpl is the Planck scale. This is in accord with the weak-gravity conjecture proposed recently. We also study the scale dependence of the gauge theory prepotential from its embedding into supergravity.