Showing papers by "Yuji Tachikawa published in 2009"
TL;DR: In this article, the authors describe configurations of 5-brane and 7-branes which realize, when compactified on a circle, new isolated four-dimensional N = 2 superconformal field theories recently constructed by Gaiotto.
Abstract: We describe configurations of 5-branes and 7-branes which realize, when compactified on a circle, new isolated four-dimensional N=2 superconformal field theories recently constructed by Gaiotto. Our diagrammatic method allows to easily count the dimensions of Coulomb and Higgs branches, with the help of a generalized s-rule. We furthermore show that superconformal field theories with E6, E7, E8 flavor symmetry can be analyzed in a uniform manner in this framework; in particular we realize these theories at infinitely strongly-coupled limits of quiver theories with SU gauge groups.
324 citations
TL;DR: In this article, the authors describe configurations of 5-brane and 7-branes which realize, when compactified on a circle, new isolated four-dimensional = 2 superconformal field theories recently constructed by Gaiotto.
Abstract: We describe configurations of 5-branes and 7-branes which realize, when compactified on a circle, new isolated four-dimensional = 2 superconformal field theories recently constructed by Gaiotto. Our diagrammatic method allows to easily count the dimensions of Coulomb and Higgs branches, with the help of a generalized s-rule. We furthermore show that superconformal field theories with E6,7,8 flavor symmetry can be analyzed in a uniform manner in this framework; in particular we realize these theories at infinitely strongly-coupled limits of quiver theories with SU gauge groups.
313 citations
TL;DR: In this paper, the authors conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class of N=2 SCFTs.
Abstract: We conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class of N=2 SCFTs recently defined by one of the authors. We conduct extensive tests of the conjecture at genus 0,1.
170 citations
TL;DR: In this article, the authors constructed four-dimensional = 2 superconformal quiver gauge theories with alternating SO and USp gauge groups as compactifications of the six-dimensional DN theory with defects.
Abstract: 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.
137 citations
TL;DR: In this article, four-dimensional N = 2 superconformal quiver gauge theories with alternating SO and USp gauge groups were constructed as compactifications of the six-dimensional D_N theory with defects, which can be used to analyze infinitely strongly coupled limits and S-dualities of such theories.
Abstract: We realize four-dimensional N=2 superconformal quiver gauge theories with alternating SO and USp gauge groups as compactifications of the six-dimensional D_N 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 N=2 superconformal field theories with SO(2N)^3 flavor symmetry.
119 citations
TL;DR: In this article, the asymptotic Virasoro symmetry was studied on the near-horizon region of extremal four-dimensional black hole solutions of gravity theories with higher-derivative corrections.
Abstract: 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.
115 citations
TL;DR: In this article, a conformal, acceleration-extended, Galilei algebra, which arises also as a contraction of the relativistic conformal algebra, is discussed, where boosts do not commute.
Abstract: We discuss non-relativistic conformal algebras generalizing the Schr\"odinger algebra. One instance of these algebras is a conformal, acceleration-extended, Galilei algebra, which arises also as a contraction of the relativistic conformal algebra. In two dimensions, this admits an "exotic" central extension, whereby boosts do not commute. We study general properties of non-relativistic conformal field theories with such symmetry. We realize geometrically the symmetry in terms of a metric invariant under the exotic conformal Galilei algebra, although its signature is neither Lorentzian nor Euclidean. We comment on holographic-type calculations in this background.
95 citations
TL;DR: In this article, the role of extended objects in Liouville theory, including surface operators and line operators, has been investigated under the assumption of a duality between four-dimensional N = 2 GAs.
Abstract: Recently, a duality between Liouville theory and four dimensional N=2 gauge theory has been uncovered by some of the authors. We consider the role of extended objects in gauge theory, surface operators and line operators, under this correspondence. We map such objects to specific operators in Liouville theory. We employ this connection to compute the expectation value of general supersymmetric 't Hooft-Wilson line operators in a variety of N=2 gauge theories.
67 citations
TL;DR: In this article, it was shown that the central charges of a four-dimensional superconformal field theory (SCFT) are related to those of a one-dimensional SCFT by a universal linear transformation, provided that there are no accidental symmetries in the infrared.
Abstract: We show that when a four-dimensional $\mathcal{N}=2$ superconformal field theory (SCFT) flows to an $\mathcal{N}=1$ SCFT via giving a mass to the adjoint chiral superfield in a vector multiplet with marginal coupling, the central charges $a$ and $c$ of the $\mathcal{N}=2$ theory are related to those of the $\mathcal{N}=1$ theory by a universal linear transformation as long as there are no accidental symmetries in the infrared. In the large $N$ limit, this relationship implies that the central charges obey ${a}_{\mathrm{IR}}/{a}_{\mathrm{UV}}={c}_{\mathrm{IR}}/{c}_{\mathrm{UV}}=27/32$. This gives a physical explanation to many examples of this number found in the literature, and also suggests the existence of a flow between some theories not previously thought to be connected.
66 citations
TL;DR: In this article, a set of tools that can be used to explore the superconformal phases of these theories are described, and the contribution of such non-Lagrangian sectors to the NSVZ beta function is elucidated.
Abstract: In theories without known Lagrangian descriptions, knowledge of the global symmetries is often one of the few pieces of information we have at our disposal. Gauging (part of) such global symmetries can then lead to interesting new theories, which are usually still quite mysterious. In this work, we describe a set of tools that can be used to explore the superconformal phases of these theories. In particular, we describe the contribution of such non-Lagrangian sectors to the NSVZ beta-function, and elucidate the counting of marginal deformations. We apply our techniques to N=1 theories obtained by mass deformations of the N=2 conformal theories recently found by Gaiotto. Because the basic building block of these theories is a triskelion, or trivalent vertex, we dub them "Sicilian gauge theories." We identify these N=1 theories as compactifications of the six-dimensional A_N (2,0) theory on Riemann surfaces with punctures and SU(2) Wilson lines. These theories include the holographic duals of the N=1 supergravity solutions found by Maldacena and Nunez.
47 citations
TL;DR: In this paper, the asymptotic Virasoro symmetry was studied on the near-horizon region of extremal four-dimensional black hole solutions of gravity theories with higher-derivative corrections.
Abstract: 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.