APPLICATIONS OF DUALITY THEORY TO AGRICULTURE

Research Methods/ Statistical Methods,

The Thermodynamic Potentials of Kerr-AdS Black Holes and their CFT Duals

String or M-theory in the background of Kerr-AdS black holes is thought to be dual to the large n limit of certain conformal field theories on a rotating sphere at finite temperature. The five dimensional black hole is associated to N=4 supersymmetric Yang-Mills theory on a rotating three-sphere and the four dimensional one to the superconformal field theory of coinciding M2 branes on a rotating two-sphere. The thermodynamic potentials can be expanded in inverse powers of the radius of the sphere. We compute the leading and subleading terms of this expansion in the field theory at one loop and compare them to the corresponding supergravity expressions. The ratios between these terms at weak and strong coupling turns out not to depend on the rotation parameters in the case of N=4 SYM. For the field theory living on one M2 brane we find a subleading logarithmic term. No such term arises from the supergravity calculation.Comment: 14 pages (harvmac b-mode), signs corrected, minor changes otherwis

A Note on the String Analog of N=2N=2 Super-Symmetric Yang-Mills

A connection between the conifold locus of the type II string on the $W\:P_{11226}^4$ Calabi-Yau manifold and the geometry of the quantum moduli of $N = 2$ $SU(2)$ super Yang-Mills is presented. This relation is obtained from the anomalous behaviour of the $SU(2)$ super Yang-Mills special coordinates under $S$-duality transformation in $Sl(2;Z) / \Gamma_2$.Comment: 7 pages, Late

From UV/IR mixing to closed strings

It was shown in hep-th/0301099 that the leading UV/IR mixing effects in noncommutative gauge theories on D-branes are able to capture information about the closed string spectrum of the parent string theory. The analysis was carried out for D-branes on nonsupersymmetric C^3/Z_N orbifolds of Type IIB. In this paper we consider D-branes on twisted circles compactifications of Type II string theory. We find that the signs of the leading UV/IR mixing effects know about the mass gap between the lowest modes in NSNS and RR closed string towers. Moreover, the relevant piece of the field theory effective action can be reproduced purely in the language of closed strings. Remarkably this approach unifies in a single structure, that of a closed string exchange between D-branes, both the leading planar and nonplanar effects associated to the absence of supersymmetry.Comment: 28 pages, 4 figures, LaTex; v2 references added, misprints correcte

A Family of N=1 SU(N)^k Theories from Branes at Singularities

We obtain N=1 SU(N)^k gauge theories with bifundamental matter and a quartic superpotential as the low energy theory on D3-branes at singular points. These theories generalize that on D3-branes at a conifold point, studied recently by Klebanov and Witten. For k=3 the defining equation of the singular point is that of an isolated D_4 singularity. For k>3 we obtain a family of multimodular singularities. The considered SU(N)^k theories flow in the infrared to a non-trivial fixed point. We analyze the AdS/CFT correspondence for our examples.Comment: 18 pages, 1 figure, TeX; v2 minor change