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

On Sp(0) factors and orientifolds

We discuss the geometric engineering of SO/Sp gauge theories with symmetric or antisymmetric tensor matter and show that the `mysterious' rank zero gauge group factors observed by a few authors can be traced back to the effects of an orientifold which survives the geometric transition. By mapping the Konishi constraints of such models to those of the U(N) theory with adjoint matter, we show that the required shifts in the ranks of the unbroken gauge group components is due to the flux contribution of the orientifold after the transition.Comment: 14 page

Topological Strings from WZW Models

We show that the BRST structure of the topological string is encoded in the ``small'' $N=4$ superconformal algebra, enabling us to obtain, in a non-trivial way, the string theory from hamiltonian reduction of $A(1|1)$. This leads to the important conclusion that not only ordinary string theories, but topological strings as well, can be obtained, or even defined, by hamiltonian reduction from WZW models. Using two different gradations, we find either the standard $N=2$ minimal models coupled to topological gravity, or an embedding of the bosonic string into the topological string. We also comment briefly on the generalization to super Lie algebras $A(n|n)$.Comment: 14p, late

Chiral field theories from conifolds

We discuss the geometric engineering and large n transition for an N=1 U(n) chiral gauge theory with one adjoint, one conjugate symmetric, one antisymmetric and eight fundamental chiral multiplets. Our IIB realization involves an orientifold of a non-compact Calabi-Yau A_2 fibration, together with D5-branes wrapping the exceptional curves of its resolution as well as the orientifold fixed locus. We give a detailed discussion of this background and of its relation to the Hanany-Witten realization of the same theory. In particular, we argue that the T-duality relating the two constructions maps the Z_2 orientifold of the Hanany-Witten realization into a Z_4 orientifold in type IIB. We also discuss the related engineering of theories with SO/Sp gauge groups and symmetric or antisymmetric matter.Comment: 34 pages, 8 figures, v2: References added, minor correction

Chiral field theories, Konishi anomalies and matrix models

We study a chiral N=1, U(N) field theory in the context of the Dijkgraaf-Vafa correspondence. Our model contains one adjoint, one conjugate symmetric and one antisymmetric chiral multiplet, as well as eight fundamentals. We compute the generalized Konishi anomalies and compare the chiral ring relations they induce with the loop equations of the (intrinsically holomorphic) matrix model defined by the tree-level superpotential of the field theory. Surprisingly, we find that the matrix model is well-defined only if the number of flavors equals two! Despite this mismatch, we show that the 1/N expansion of the loop equations agrees with the generalized Konishi constraints. This indicates that the matrix model - gauge theory correspondence should generally be modified when applied to theories with net chirality. We also show that this chiral theory produces the same gaugino superpotential as a nonchiral SO(N) model with a single symmetric multiplet and a polynomial superpotential.Comment: 43 page

Puzzles for Matrix Models of Chiral Field Theories

We summarize the field-theory/matrix model correspondence for a chiral N=1 model with matter in the adjoint, antisymmetric and conjugate symmetric representations as well as eight fundamentals to cancel the chiral anomaly. The associated holomorphic matrix model is consistent only for two fundamental fields, which requires a modification of the original Dijkgraaf-Vafa conjecture. The modified correspondence holds in spite of this mismatch.Comment: Contribution to the proceedings of the 36th International Symposium Ahrenshoop, Berlin, August 26-30, 2003; 6 Page

(Anti)symmetric matter and superpotentials from IIB orientifolds

We study the IIB engineering of N=1 gauge theories with unitary gauge group and matter in the adjoint and (anti)symmetric representations. We show that such theories can be obtained as Z2 orientifolds of Calabi-Yau A2 fibrations, and discuss the explicit T-duality transformation to an orientifolded Hanany-Witten construction. The low energy dynamics is described by a geometric transition of the orientifolded background. Unlike previously studied cases, we show that the orientifold 5-`plane' survives the transition, thus bringing a nontrivial contribution to the effective superpotential. We extract this contribution by using matrix model results and compare with geometric data. A Higgs branch of our models recovers the engineering of SO/Sp theories with adjoint matter through an O5-`plane' T-dual to an O6-plane. We show that the superpotential agrees with that produced by engineering through an O5-`plane' dual to an O4-plane, even though the orientifold of this second construction is replaced by fluxes after the transition.Comment: 40 page