Triangle Anomalies from Einstein Manifolds

The triangle anomalies in conformal field theory, which can be used to determine the central charge a, correspond to the Chern-Simons couplings of gauge fields in AdS under the gauge/gravity correspondence. We present a simple geometrical formula for the Chern-Simons couplings in the case of type IIB supergravity compactified on a five-dimensional Einstein manifold X. When X is a circle bundle over del Pezzo surfaces or a toric Sasaki-Einstein manifold, we show that the gravity result is in perfect agreement with the corresponding quiver gauge theory. Our analysis reveals an interesting connection with the condensation of giant gravitons or dibaryon operators which effectively induces a rolling among Sasaki-Einstein vacua.Comment: 30 pages, 5 figures; published versio

Comments on the non-conformal gauge theories dual to Ypq manifolds

We study the infrared behavior of the entire class of Y(p,q) quiver gauge theories. The dimer technology is exploited to discuss the duality cascades and support the general belief about a runaway behavior for the whole family. We argue that a baryonic classically flat direction is pushed to infinity by the appearance of ADS-like terms in the effective superpotential. We also study in some examples the IR regime for the L(a,b,c) class showing that the same situation might be reproduced in this more general case as well.Comment: 48 pages, 27 figures; updated reference

Comments on Anomalies and Charges of Toric-Quiver Duals

We obtain a simple expression for the triangle `t Hooft anomalies in quiver gauge theories that are dual to toric Sasaki-Einstein manifolds. We utilize the result and simplify considerably the proof concerning the equivalence of a-maximization and Z-minimization. We also resolve the ambiguity in defining the flavor charges in quiver gauge theories. We then compare coefficients of the triangle anomalies with coefficients of the current-current correlators and find perfect agreement.Comment: 22 pages, 3 figure

R-charges from toric diagrams and the equivalence of a-maximization and Z-minimization

We conjecture a general formula for assigning R-charges and multiplicities for the chiral fields of all gauge theories living on branes at toric singularities. We check that the central charge and the dimensions of all the chiral fields agree with the information on volumes that can be extracted from toric geometry. We also analytically check the equivalence between the volume minimization procedure discovered in hep-th/0503183 and a-maximization, for the most general toric diagram. Our results can be considered as a very general check of the AdS/CFT correspondence, valid for all superconformal theories associated with toric singularities.Comment: 43 pages, 17 figures; minor correction

Nehru’s Bandung moment: India and the convening of the 1955 Asian-African conference

This article explores Jawaharlal Nehru’s role in convening the 1955 Bandung Conference. Drawing upon previously embargoed Indian and Western government records, it sheds light on a largely overlooked aspect of Nehru’s Cold War diplomacy. By doing so, it shows that Nehru did not attach, at least initially, much importance to Indonesia’s calls for an Asian-African conference. Only in late 1954 did he show more interest in the Indonesian proposal. Three factors pushed Nehru in this direction: his reluctance to embarrass Indonesia, his concerns about American regional policy and his desire to exploit China’s support for peaceful coexistence. Confronted with renewed regional tensions but able to capitalize on Beijing’s new-found reasonableness, Nehru threw India’s diplomatic weight behind Indonesia’s proposal with the view to furthering his vision of “areas of peace.” Nehru’s “Bandung moment,” however, was short-lived. Although the Bandung Conference appeared to have advanced India’s national interests in the short term, its benefits were more questionable in the long run. In the end, India was unable to tie China down to its regional vision and protect itself against Chinese belligerence. Faced with a mounting Chinese challenge, Nehru’s strategy, centered upon nonaligned peaceful coexistence, manifested all its limitations

From Sasaki-Einstein spaces to quivers via BPS geodesics: Lpqr

The AdS/CFT correspondence between Sasaki-Einstein spaces and quiver gauge theories is studied from the perspective of massless BPS geodesics. The recently constructed toric Lpqr geometries are considered: we determine the dual superconformal quivers and the spectrum of BPS mesons. The conformal anomaly is compared with the volumes of the manifolds. The U(1)^2_F x U(1)_R global symmetry quantum numbers of the mesonic operators are successfully matched with the conserved momenta of the geodesics, providing a test of AdS/CFT duality. The correspondence between BPS mesons and geodesics allows to find new precise relations between the two sides of the duality. In particular the parameters that characterize the geometry are mapped directly to the parameters used for a-maximization in the field theory. The analysis simplifies for the special case of the Lpqq models, which are shown to correspond to the known "generalized conifolds". These geometries can break conformal invariance through toric deformations of the complex structure.Comment: 30 pages, 8 figures, LaTeX. v2: One more figure. References added, typos correcte

Baryonic Generating Functions

We show how it is possible to use the plethystic program in order to compute baryonic generating functions that count BPS operators in the chiral ring of quiver gauge theories living on the world volume of D branes probing a non compact CY manifold. Special attention is given to the conifold theory and the orbifold C^2/Z_2 times C, where exact expressions for generating functions are given in detail. This paper solves a long standing problem for the combinatorics of quiver gauge theories with baryonic moduli spaces. It opens the way to a statistical analysis of quiver theories on baryonic branches. Surprisingly, the baryonic charge turns out to be the quantized Kahler modulus of the geometry.Comment: 44 pages, 7 figures; fonts change

Near-flat space limit and Einstein manifolds

We study the near-flat space limit for strings on AdS(5)xM(5), where the internal manifold M(5) is equipped with a generic metric with U(1)xU(1)xU(1) isometry. In the bosonic sector, the limiting sigma model is similar to the one found for AdS(5)xS(5), as the global symmetries are reduced in the most general case. When M(5) is a Sasaki-Einstein space like T(1,1), Y(p,q) and L(p,q,r), whose dual CFT's have N=1 supersymmetry, the near-flat space limit gives the same bosonic sector of the sigma model found for AdS(5)xS(5). This indicates the generic presence of integrable subsectors in AdS/CFT.Comment: 30 pages, 1 figur

Zonotopes and four-dimensional superconformal field theories

The a-maximization technique proposed by Intriligator and Wecht allows us to determine the exact R-charges and scaling dimensions of the chiral operators of four-dimensional superconformal field theories. The problem of existence and uniqueness of the solution, however, has not been addressed in general setting. In this paper, it is shown that the a-function has always a unique critical point which is also a global maximum for a large class of quiver gauge theories specified by toric diagrams. Our proof is based on the observation that the a-function is given by the volume of a three dimensional polytope called "zonotope", and the uniqueness essentially follows from Brunn-Minkowski inequality for the volume of convex bodies. We also show a universal upper bound for the exact R-charges, and the monotonicity of a-function in the sense that a-function decreases whenever the toric diagram shrinks. The relationship between a-maximization and volume-minimization is also discussed.Comment: 29 pages, 15 figures, reference added, typos corrected, version published in JHE