Showing papers by "Yuji Tachikawa published in 2008"

Comments on string theory backgrounds with non-relativistic conformal symmetry

Abstract: We consider non-relativistic conformal quantum mechanical theories that arise by doing discrete light cone quantization of field theories. If the field theory has a gravity dual, then the conformal quantum mechanical theory can have a gravity dual description in a suitable finite temperature and finite density regime. Using this we compute the thermodynamic properties of the system. We give an explicit example where we display both the conformal quantum mechanical theory as well as the gravity dual. We also discuss the string theory embedding of certain backgrounds with non-relativistic conformal symmetry that were recently discussed. Using this, we construct finite temperature and finite density solutions, with asymptotic non-relativistic conformal symmetry. In addition, we derive consistent Kaluza-Klein truncations of type IIB supergravity to a five dimensional theory with massive vector fields.

Central charges of N=2 superconformal field theories in four dimensions

Abstract: We present a general method for computing the central charges a and c of N=2 superconformal field theories corresponding to singular points in the moduli space of N=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 N=4 SU(N), 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.

Central charges of = 2 superconformal field theories in four dimensions

Abstract: 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.

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

Abstract: 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.

Classification of N=6 superconformal theories of ABJM type

Abstract: Studying the supersymmetry enhancement mechanism of Aharony, Bergman, Jafferis and Maldacena, we find a simple condition on the gauge group generators for the matter fields. We analyze all possible compact Lie groups and their representations. The only allowed gauge groups leading to the manifest N=6 supersymmetry are, up to discrete quotients, SU(n) x U(1), Sp(n) x U(1), SU(n) x SU(n), and SU(n) x SU(m) x U(1) with possibly additional U(1)'s. Matter representations are restricted to be the (bi)fundamentals. As a byproduct we obtain another proof of the complete classification of the three algebras considered by Bagger and Lambert.

Comments on string theory backgrounds with non-relativistic conformal symmetry

Abstract: We consider non-relativistic conformal quantum mechanical theories that arise by doing discrete light cone quantization of field theories. If the field theory has a gravity dual, then the conformal quantum mechanical theory can have a gravity dual description in a suitable finite temperature and finite density regime. Using this we compute the thermodynamic properties of the system. We give an explicit example where we display both the conformal quantum mechanical theory as well as the gravity dual. We also discuss the string theory embedding of certain backgrounds with non-relativistic conformal symmetry that were recently discussed. Using this, we construct finite temperature and finite density solutions, with asymptotic non-relativistic conformal symmetry. In addition, we derive consistent Kaluza-Klein truncations of type IIB supergravity to a five dimensional theory with massive vector fields.

A counterexample to the a-'theorem'

Abstract: We exhibit a renormalization group flow for a four-dimensional gauge theory along which the conformal central charge a increases. The flow connects the maximally superconformal point of an = 2 gauge theory with gauge group SU(N+1) and Nf = 2N flavors in the ultraviolet, to a strongly-coupled superconformal point of the SU(N) gauge theory with Nf = 2N massless flavors in the infrared. Our example does not contradict the proof of the a-theorem via a-maximization, due to the presence of accidental symmetries in the infrared limit. Nor does it contradict the holographic a-theorem, because these gauge theories do not possess weakly-curved holographic duals.

Argyres-Seiberg duality and the Higgs branch

Abstract: We demonstrate the agreement between the Higgs branches of two N=2 theories proposed by Argyres and Seiberg to be S-dual, namely the SU(3) gauge theory with six quarks, and the SU(2) gauge theory with one pair of quarks coupled to the superconformal theory with E_6 flavor symmetry. In mathematical terms, we demonstrate the equivalence between a hyperkaehler quotient of a linear space and another hyperkaehler quotient involving the minimal nilpotent orbit of E_6, modulo the identification of the twistor lines.

A-D-E quivers and baryonic operators

Abstract: We study baryonic operators of the gauge theory on multiple D3-branes at the tip of the conifold orbifolded by a discrete subgroup Γ of SU(2). The string theory analysis predicts that the number and the order of the fixed points of Γ acting on S2 are directly reflected in the spectrum of baryonic operators on the corresponding quiver gauge theory constructed from two Dynkin diagrams of the corresponding type. We confirm the prediction by utilizing techniques to enumerate baryonic operators of the quiver gauge theory which includes the gauge groups with different ranks. We also find that the Seiberg dualities act on the baryonic operators in a non-Abelian fashion.

A-d-e quivers and baryonic operators

Abstract: We study baryonic operators of the gauge theory on multiple D3-branes at the tip of the conifold orbifolded by a discrete subgroup of SU(2). The string theory analysis predicts that the number and the order of the fixed points of this discrete subgroup acting on S2 are directly reflected in the spectrum of baryonic operators on the corresponding quiver gauge theory constructed from two Dynkin diagrams of the corresponding type. We confirm the prediction by utilizing techniques to enumerate baryonic operators of the quiver gauge theory which includes the gauge groups with different ranks.

Geometric engineering limit and weak gravity conjecture

Abstract: We analyze the coupled 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.