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We compute the next-to-leading order term in the long-distance expansion of the mutual information for free scalars in three space-time dimensions. The geometry considered is two disjoint disks separated by a distance $r$ between their centers. No evidence for non-analyticity in the R\'enyi parameter $n$ for the continuation $n \rightarrow 1$ in the next-to-leading order term is found., Comment: 15 pages, This version contains few extra references, some technical material has been move to appendices, and other minor modifications to match with the version accepted for publication

As a consequence of the AdS/CFT correspondence, planar ${\cal N} =4$ super Yang-Mills SU(N) theory is expected to exhibit stringy behavior and multi-Regge asymptotic. In this paper we extend our recent investigation to consider issues of analyticity, a central feature of Regge asymptotics. We contrast flat-space open string theory in the planar limit with the ${\cal N}=4$ super Yang-Mills theory, as represented by the Bern, Dixon and Smirnov \cite{Bern:2005iz} (BDS) conjecture for n-gluon scattering, believed to be exact for $n=4,5$ and modified only by a function of cross-ratios for $n\geq 6$. It is emphasized that multi-Regge factorization should be applied to trajectories with definite signature. A variety of analyticity and factorization constraints realized in flat space string theory are not satisfied by the BDS conjecture, at least when the exponential factors are truncate in the infra-red regulator below $O(\epsilon)$., Comment: Published version of the paper, which includes an expanded discussion on Steinmann Relation for 5-point function, (sect. 4.3 and footnotes #9 and #10) as well as additional clarifying comments on how this work compares to other recent related works in the concluding section. 74 pages, 17 figures

We derive an ABDK-like relation between the one- and two-loop four-graviton amplitudes in N = 8 supergravity. Specifically we show that the infrared-divergent part of the two-loop amplitude is one-half the square of the one-loop amplitude, suggesting an exponential structure for IR divergences. The difference between the two-loop amplitude and one-half the square of the full one-loop amplitude is therefore finite, and expressible in a relatively simple form. We give arguments for generalizations to higher loops and n-point functions, suggesting that the exponential of the full one-loop amplitude may be corrected, to low orders, by only simple finite terms.

It is shown that the four-gluon scattering amplitude for N=4 supersymmetric Yang–Mills theory in the planar limit can be written, in both the weak- and strong-coupling limits, as a reggeized amplitude, with a parent trajectory and an infinite number of daughter trajectories. This result is not evident a priori, and relies crucially on the fact that the leading IR-divergence and the finite log2(s/t)-dependent piece of the amplitude are characterized by the same function for all values of the coupling, as conjectured by Bern, Dixon, and Smirnov, and proved by Alday and Maldacena in the strong-coupling limit. We use the Alday–Maldacena result to determine the exact strong-coupling Regge trajectory.

We analyze the level-rank duality of ω c -twisted D-branes of su ˆ ( N ) K (when N and K > 2 ). When N or K is even, the duality map involves Z 2 -cominimal equivalence classes of twisted D-branes. We prove the duality of the spectrum of an open string stretched between ω c -twisted D-branes, and ascertain the relation between the charges of level-rank-dual ω c -twisted D-branes.

The consequences of level-rank duality for untwisted D-branes on an SU(N) group manifold are explored. Relations are found between the charges of D-branes (which are classified by twisted K-theory) belonging to su(N)_K and su(K)_N WZW theories, in the case of odd N+K. An isomorphism between the charge algebras is also demonstrated in this case., Comment: 15 pages. v2 and v3: references added. v4: proof clarified and minor typos fixed

We consider large N zero-coupling d-dimensional U ( N ) gauge theories, with N f matter fields in the fundamental representation on a compact spatial manifold S d − 1 × time, with N f / N finite. The Gauss' law constraint induces interactions among the fields, in spite of the zero-coupling. This class of theories undergo a 3rd order deconfinement phase transition at a temperature T c proportional to the inverse length scale of the compact manifold. The low-temperature phase has a free-energy of O ( N f 2 ) , interpreted as that of a gas of (color singlet) mesons and glueballs. The high-temperature (deconfinement) phase has a free energy of order N 2 f ( N f / N , T ) , which is interpreted as that of a gas of gluons and of fundamental and anti-fundamental matter states. This suggests the existence of a dual string theory, and a transition to a black hole at high temperature.

Motivated by the work of Klebanov and Polyakov [hep-th/0210114] on the relationship of the large N O(N) vector model in three-dimensions to AdS_4 and higher spin representations, we attempt to find analogous connections for AdS_5. Since the usual O(N) vector model in four-dimensions is inconsistent, we consider the (consistent) large N gauged vector model and a N=1 supersymmetric analogue in four-dimensions. Both these theories have UV and IR fixed points, and are candidates for a (\alpha')^-1 expansion in AdS_5, a conjectured AdS_5/CFT correspondence and higher-spin representations in the bulk theory., Comment: 18 pages, LaTex, 1 figure, v. 2, references added; a minor correction

Using matrix-model methods we study three different N =2 models: U(N)×U(N) with matter in the bifundamental representation, U(N) with matter in the symmetric representation, and U(N) with matter in the antisymmetric representation. We find that the (singular) cubic Seiberg–Witten curves (and associated Seiberg–Witten differentials) implied by the matrix models, although of a different form from the ones previously proposed using M-theory, can be transformed into the latter and are thus physically equivalent. We also calculate the one-instanton corrections to the gauge-coupling matrix using the perturbative expansion of the matrix model. For the U(N) theories with symmetric or antisymmetric matter we use the modified matrix-model prescription for the gauge-coupling matrix discussed in our paper: Cubic curves from matrix models and generalized Konishi anomalies ( hep-th/0303268 ). Moreover, in the matrix model for the U(N) theory with antisymmetric matter, one is required to expand around a different vacuum than one would naively have anticipated. With these modifications of the matrix-model prescription, the results of this paper are in complete agreement with those of Seiberg–Witten theory obtained using M-theory methods.

We perform a completely perturbative matrix model calculation of the physical low-energy quantities of the N=2 U(N) gauge theory. Within the matrix model framework we propose a perturbative definition of the periods a_i in terms of certain tadpole diagrams, and check our conjecture up to first order in the gauge theory instanton expansion. The prescription does not require knowledge of the Seiberg-Witten differential or curve. We also compute the N=2 prepotential F(a) perturbatively up to the first-instanton level finding agreement with the known result.

We study the N=1 Sp(2N+2M)xSp(2N) cascading gauge theory on a stack of N physical and M fractional (half) D3-branes at the singularity of an orientifolded conifold. In addition to the D3-branes and an O7-plane, the background contains eight D7-branes, which give rise to matter in the fundamental representation of the gauge group. The moduli space of the gauge theory is analyzed and its structure is related to the brane configurations in the dual type IIB theory and in type IIA/M-theory.

We find the classical supersymmetric vacuum states of a class of N =1 ∗ field theories obtained by mass deforming superconformal models with simple gauge groups and N =4 or N =2 supersymmetry. In particular, new classical vacuum states for mass-deformed N =4 models with Sp(2N) and SO(N) gauge symmetry are found. We also derive the classical vacua for various mass-deformed N =2 models with Sp(2N) and SU(N) gauge groups and antisymmetric (and symmetric) hypermultiplets. We suggest interpretations of the mass-deformed vacua in terms of three-branes expanded into five-brane configurations.

The renormalization group flows of the coupling constants for the gauged U(N) vector model, with N_f massless fermions in the defining representation, are studied in the large N limit, to all orders in the scalar coupling lambda, leading order in 1/N, and lowest two orders in the gauge coupling g^2. It is shown that the restrictions of asymptotic freedom, and the reality of the coupling constants throughout the flows, places important restrictions on N_f/N. For the case with massless mesons, these conditions are sufficiently restrictive to imply the existence of an infrared fixed-point (g_*,lambda_*) in both couplings. Thus, the consistent massless theory is scale invariant, and in a non-abelian Coulomb phase. The case of massive mesons, and of spontaneously broken symmetry is also discussed, with similar, but not identical, conclusions. Speculations related to the possibility that there is a non-perturbative (in g^2) breakdown of chiral symmetry are presented., 15 pages, plain Latex, one figure added

A calculation of the renormalization group improved effective potential for the gauged U(N) vector model, coupled to $N_f$ fermions in the fundamental representation, computed to leading order in 1/N, all orders in the scalar self-coupling $\lambda$, and lowest order in gauge coupling $g^2$, with $N_f$ of order $N$, is presented. It is shown that the theory has two phases, one of which is asymptotically free, and the other not, where the asymptotically free phase occurs if $0 < \lambda /g^2 < {4/3} (\frac{N_f}{N} - 1)$, and $\frac{N_f}{N} < {11/2}$. In the asymptotically free phase, the effective potential behaves qualitatively like the tree-level potential. In the other phase, the theory exhibits all the difficulties of the ungauged $(g^2 = 0)$ vector model. Therefore the theory appears to be consistent (only) in the asymptotically free phase., Comment: Latex, 18 pages plus 3 figures using epsf. Substantially revised to correct a factor of 2 error in the previous version of equation (2.5b). This has significant effects on the results. The model has also been revised to include fermions

The path integral computation of field strength correlation functions for two-dimensional Yang–Mills theories over Riemann surfaces is studied. The calculation is carried out by Abelianization, which leads to correlators that are topological. They are nontrivial as a result of the topological obstructions to the Abelianization. It is shown in the large N limit on the sphere that the correlators undergo second order phase transitions at the critical point. Our results are applied to a computation of contractible Wilson loops.

A new method to obtain the Picard-Fuchs equations of effective, N=2 supersymmetric gauge theories with massive matter hypermultiplets in the fundamental representation is presented. It generalises a previously described method to derive the Picard-Fuchs equations of both pure super Yang-Mills and supersymmetric gauge theories with massless matter hypermultiplets. The techniques developed are well suited to symbolic computer calculations., Comment: 29 pages, uses phyzzx.tex

A new method to obtain the Picard-Fuchs equations of effective $N = 2$ supersymmetric gauge theories in 4 dimensions is developed. It includes both pure super Yang-Mills and supersymmetric gauge theories with massless matter hypermultiplets. It applies to all classical gauge groups, and directly produces a decoupled set of second-order, partial differential equations satisfied by the period integrals of the Seiberg-Witten differential along the 1-cycles of the algebraic curves describing the vacuum structure of the corresponding $N = 2$ theory., Latex version, 43 pages, a few cosmetic changes and some references added

We examine the high energy (Regge) limit of gravitational scattering using a Wilson line approach previously used in the context of non-Abelian gauge theories. Our aim is to clarify the nature of the Reggeization of the graviton and the interplay between this Reggeization and the so-called eikonal phase which determines the spectrum of gravitational bound states. Furthermore, we discuss finite corrections to this picture. Our results are of relevance to various supergravity theories, and also help to clarify the relationship between gauge and gravity theories., 33 pages, 5 figures

The infrared singularities of gravitational amplitudes are one-loop exact, in that higher-loop divergences are characterized by the exponential of the one-loop divergence. We show that the contributions to SU(N) gauge-theory amplitudes that are most-subleading in the 1/N expansion are also one-loop exact, provided that the dipole conjecture holds. Possible corrections to the dipole conjecture, beginning at three loops, could violate one-loop-exactness, though would still maintain the absence of collinear divergences. We also demonstrate a relation between L-loop four-point N=8 supergravity and most-subleading-color N=4 SYM amplitudes that holds for the two leading IR divergences, O(1/\epsilon^L) and O(1/\epsilon^{L-1}), but breaks down at O(1/\epsilon^{L-2})., Comment: 23 pages, no figures

We demonstrate that the large-N expansion of Wilson loop expectation values in SO(N) and Sp(N) Yang-Mills theory on orientable and nonorientable surfaces has a natural description as a weighted sum over covers of the given surface. The sum takes the form of the perturbative expansion of an open string theory. The derivation makes contact with the classification of branched covers by Gabai and Kazez. Comparison with the analogous results for the chiral sectors of QCD_2 is instructive for both cases., 24 pages, LaTeX, no figures, minor changes for published version

A cutoff version of the λϕ4 O(N) model is considered to leading order in 1/N with particular attention paid to the effective potential, which is surprisingly rich in structure. With suitable restriction on a background classical field, one finds a phenomenologically viable model with spontaneously broken symmetry, a potential bounded below, and amplitudes free of tachyons. The model has an O(N − 1) singlet resonance in both weak and strong couplings, which can be interpreted as the Higgs meson in applications. Further, an unphysical resonance, which can be used to define a triviality scale for the model, appears at a mass above the cutoff mass Λ. The phenomenological aspects of our discussion are consistent with previous studies, whose results are obtained by somewhat different methods. The question of the double-scaling limit for the cutoff model is considered as an application of the effective potential. It is shown that the double-scaling limit is not possible.

We consider the multi-Regge limit for N=4 SYM NMHV leading color amplitudes in two different formulations: the BFKL formalism for multi-Regge amplitudes in leading logarithm approximation, and superconformal N=4 SYM amplitudes. It is shown that the two approaches agree to two-loops for the 2->4 and 3->3 six-point amplitudes. Predictions are made for the multi-Regge limit of three loop 2->4 and 3->3 NMHV amplitudes, as well as a particular sub-set of two loop 2 ->2 +n N^kMHV amplitudes in the multi-Regge limit in the leading logarithm approximation from the BFKL point of view., 28 pages, 3 figures

We derive a linear relation between the one-loop five-point amplitude of N=8 supergravity and the one-loop five-point subleading-color amplitudes of N=4 supersymmetric Yang-Mills theory., Comment: 17 pages, 2 figures; v2: very minor corrections

We use the relation of the one-loop subleading-color amplitudes to the one-loop $n$-point leading color amplitudes in ${\cal N}=4$ SYM, to derive a polytope interpretation for the former in the $MHV$ case, and a representation in momentum twistor space for the general $N^kMHV$ case. These techniques are explored in detail for the 5-point and 6-point amplitudes. We briefly discuss the implications for IR divergences., 30 pages, 2 figures; typos corrected, citations added; fig2 modified, fig. 1 and explanations added, mostly around eq. 2.11; version accepted in Nucl.Phys.B

We apply factorization and eikonal methods from gauge theories to scattering amplitudes in gravity. We hypothesize that these amplitudes factor into an IR-divergent soft function and an IR-finite hard function, with the former given by the expectation value of a product of gravitational Wilson line operators. Using this approach, we show that the IR-divergent part of the n-graviton scattering amplitude is given by the exponential of the one-loop IR divergence, as originally discovered by Weinberg, with no additional subleading IR-divergent contributions in dimensional regularization., 16 pages, 3 figures; v2: title change and minor rewording (published version); v3: typos corrected in eqs.(3.2),(4.1)

A number of features and applications of subleading color amplitudes of N=4 SYM theory are reviewed. Particular attention is given to the IR divergences of the subleading-color amplitudes, the relationships of N=4 SYM theory to N=8 supergravity, and to geometric interpretations of one-loop subleading color and N^k MHV amplitudes of N=4 SYM theory., Comment: 39 pages; v2: minor corrections

We show that the string representation of the QCD$_2$ partition function satisfies, by virtue of a Young-tableau-transposition symmetry, the topological constraint that any branched covering of an orientable or nonorientable surface without boundary must have an {\em even} branch point multiplicity. This statement holds for each chiral sector and requires multiple branch point behavior for the twist points, since cross-terms appear that couple twist points with odd powers of simple branch points. We obtain the same result for the complete partition function of $\son$ and $\spn$ Yang-Mills$_2$ theory., Comment: 8 pages, BRX-TH-352, JHU-TIPAC-930024, BOW-PH-101

A previously proposed two-step algorithm for calculating the expectation values of Chern-Simons graphs fails to determine certain crucial signs. The step which involves calculating tetrahedra by solving certain non- linear equations is repaired by introducing additional linear equations. As a first step towards a new algorithm for general graphs we find useful linear equations for those special graphs which support knots and links. Using the improved set of equations for tetrahedra we examine the symmetries between tetrahedra generated by arbitrary simple currents. Along the way we uncover the classical origin of simple-current charges. The improved skein relations also lead to exact identities between planar tetrahedra in level $K$ $G(N)$ and level $N$ $G(K)$ CS theories, where $G(N)$ denotes a classical group. These results are recast as identities for quantum $6j$-symbols and WZW braid matrices. We obtain the transformation properties of arbitrary graphs and links under simple current symmetries and rank-level duality. For links with knotted components this requires precise control of the braid eigenvalue permutation signs, which we obtain from plethysm and an explicit expression for the (multiplicity free) signs, valid for all compact gauge groups and all fusion products., 58 pages, BRX-TH-302

We derive a new non-singular tree-level KLT relation for the $n=5$-point amplitudes, with manifest $2(n-2)!$ symmetry, using information from one-loop amplitudes and IR divergences, and speculate how one might extend it to higher n-point functions. We show that the subleading-color ${\cal N}=4$ SYM 5-point amplitude has leading IR divergence of $1/\epsilon$, which is essential for the applications of this paper. We also propose a relation between the subleading-color ${\cal N}=4$ SYM and ${\cal N}=8$ supergravity 1-loop 5-point amplitudes, valid for the IR divergences and possibly for the whole amplitudes, using techniques similar to those used in our derivation of the new KLT relation., Comment: 18 pages, latex, no figures

We extend the analysis of Higgs-regulated planar amplitudes of N=4 supersymmetric Yang-Mills theory to four loops for the four-gluon amplitude and to two loops for the five-gluon amplitude. Our calculations are consistent with a proposed all-loop ansatz for planar MHV n-gluon amplitudes that is the analog of the BDS ansatz in dimensional regularization. In all cases considered, we have verified that the IR-finite parts of the logarithm of the amplitudes have the same dependence on kinematic variables as the corresponding functions in dimensionally-regulated amplitudes (up to overall additive constants, which we determine). We also study various Regge limits of N=4 SYM planar n-gluon amplitudes. Euclidean Regge limits of Higgs-regulated n \geq 4 amplitudes yield results similar in form to those found using dimensional regularization, but with different expressions for the gluon trajectory and Regge vertices resulting from the different regulator scheme. We also show that the Regge limit of the four-gluon amplitude is dominated at next-to-leading-log order by vertical ladder diagrams together with the class of vertical ladder diagrams with a single H-shaped insertion.

We compute the three-loop contribution to the N=4 supersymmetric Yang-Mills planar four-gluon amplitude using the recently-proposed Higgs IR regulator of Alday, Henn, Plefka, and Schuster. In particular, we test the proposed exponential ansatz for the four-gluon amplitude that is the analog of the BDS ansatz in dimensional regularization. By evaluating our results at a number of kinematic points, and also in several kinematic limits, we establish the validity of this ansatz at the three-loop level. We also examine the Regge limit of the planar four-gluon amplitude using several different IR regulators: dimensional regularization, Higgs regularization, and a cutoff regularization. In the latter two schemes, it is shown that the leading logarithmic (LL) behavior of the amplitudes, and therefore the lowest-order approximation to the gluon Regge trajectory, can be correctly obtained from the ladder approximation of the sum of diagrams. In dimensional regularization, on the other hand, there is no single dominant set of diagrams in the LL approximation. We also compute the NLL and NNLL behavior of the L-loop ladder diagram using Higgs regularization., Comment: 45 pages, 9 figures; v3: major revision (more stringent tests, discussion of order of limits in the Regge regime)

The SU( m | n ) K fusion ring is found. The existence of a positive trace on this ring, rather than integrability, is the common principle underlying the fusion rings of WZW models, ordinary and super. The argument proceeds by means of a combined examination of the ring of positive q -superdimensions, associated Chern-Simons observables, and several WZW correlation functions. The tensor product ring of U q ( su (m|n)) for q a root of unity admits a doubly truncated tensor product structure isomorphic to the SU( m | n ) K fusion ring in the cases we examine. The SU( m | n ) K WZW models are found to be quasi-rational (non-unitary) conformal field theories. Many important quantities in SU( m | n ) K theories are given exactly by analogous SU( m − n ) K quantities, including the conformal weights, fusion coefficients, Chern-Simons observables, and the matrix elements of modular transformations of the relevant affine supercharacters. These matrix elements are related to the fusion ring via a (slightly modified) Verlinde formula. The SU( n + N | n ) K and SU( k + K | k ) N Chern-Simons and WZW theories are related by group-level duality.

We present the duality of the fusion rule multiplicities, modular tranformation matrices and conformal weights of the Wess-Zumino-Witten models based on any of the classical affine Lie algebras SU( N ) K , Sp( N ) K and SO( N ) K under the exchange of N and K . We also exhibit the transformation properties of these quantities under the symmetries of the extended Dynkin diagrams, which play a central role in this group-level duality. We interpret these results in Chern-Simons theory, and derive identities between link observables. Several surprising results involving spinor representations of SO( N ) are proven.

It is argued that the leading Skyrme model estimate of the electric dipole moment of the neutron in chiral perturbation theory should be Dn ∼ Ncmπ2 ln mπ. To obtain this result requires a careful quantization of the pion fluctuation about the rotating skyrmion, with appropriate attention to the derivative couplings and zero modes of the model.

Planar ${\cal N} =4$ super Yang-Mills SU(N) theory is expected to exhibit stringy behavior, anticipated by the 't Hooft genus expansion and the $AdS/CFT$ correspondence. We examine the Bern-Dixon-Smirnov (BDS) conjecture for $n$-gluon amplitudes in the context of single-Regge and multi-Regge limits and show that these amplitudes have the expected Regge form in the Euclidean region., 48 pages, 8 figures; Noted added commenting on related work which appeared after the initial posting. References and clarifications added, as well as typos corrected

We study the subleading-color (nonplanar) contributions to the four-gluon scattering amplitudes in N=4 supersymmetric SU(N) Yang-Mills theory. Using the formalisms of Catani and of Sterman and Tejeda-Yeomans, we develop explicit expressions for the infrared-divergent contributions of all the subleading-color L-loop amplitudes up to three loops, and make some conjectures for the IR behavior for arbitrary L. We also derive several intriguing relations between the subleading-color one- and two-loop four-gluon amplitudes and the four-graviton amplitudes of N=8 supergravity. The exact one- and two-loop N=8 supergravity amplitudes can be expressed in terms of the one- and two-loop N-independent N=4 SYM amplitudes respectively, but the natural generalization to higher loops fails, despite having a simple interpretation in terms of the 't Hooft picture. We also find that, at least through two loops, the subleading-color amplitudes of N=4 SYM theory have uniform transcendentality (as do the leading-color amplitudes). Moreover, the N=4 SYM Catani operators, which express the IR-divergent contributions of loop amplitudes in terms of lower-loop amplitudes, are also shown to have uniform transcendentality, and to be the maximum transcendentality piece of the QCD Catani operators., Comment: 30 pages; v2: corrections in sec. 6, minor addition in sec. 3.3

We exhibit a duality of the SU(N)k WZW model under interchange of the group parameter N and the level k. The primary fields of SU(N)k and SU(k)N are related by transposition of their associated Young tableaux. The holomorphic blocks of the four-point functions of the primary fields are in one-to-one correspondence, and satisfy orthogonality and completeness relations with respect to one another. We derive these relations through a path integral realization of the SU(N)k WZW model in terms of a theory of constrained Dirac fermions.

We exhibit a duality of primary fields, conformal dimensions, braid matrices, and modular transformation matrix elements S0,λ/S0,0 (so also Weyl characters) for sequences of dual pairs (SU (N)K, SU(K)N), (SO(N)K, (SO(N)K, SO(K)N) and Sp(N)K, Sp(K)N. As a consequence an analogous duality of Chern-Simons skein relations and Wilson line observables is uncovered.

Dual relations are found between the primary fields, correlators, and conformal blocks of SU ( N ) k and SU ( k ) N WZW models, which in turn imply dual relations between the braid matrices of the two theories. These results are a consequence of the fact that the spaces of conformal blocks of SU ( N ) k and SU ( k ) N correlation functions are dual.

The relation of the gauged Wess-Zumino-Witten models describing G/H conformal field theories and the GKO construction is investigated in the BRST framework. A nilpotent operator Q is constructed and the physical spectrum and unitarity of the theory is analyzed. When H is the Cartan subalgebra of G the BRST invariant current operators (the physical currents) are shown to be the parafermionic operators.

We study the WZW, Chern-Simons, and 2d qYM theories with gauge group U(N). The U(N) WZW model is only well-defined for odd level K, and this model is shown to exhibit level-rank duality in a much simpler form than that for SU(N). The U(N) Chern-Simons theory on Seifert manifolds exhibits a similar duality, distinct from the level-rank duality of SU(N) Chern-Simons theory on S^3. When q = e^{2 pi i/(N+K)}, the observables of the 2d U(N) qYM theory can be expressed as a sum over a finite subset of U(N) representations. When N and K are odd, the qYM theory exhibits N K duality, provided q = e^{2 pi i/(N+K)} and theta = 0 mod 2 pi /(N+K)., Comment: 19 pages; v2: minor typo corrected, 1 paragraph added, published version

The Seiberg-Witten solution plays a central role in the study of N=2 supersymmetric gauge theories. As such, it provides a proving ground for a wide variety of techniques to treat such problems. In this review we concentrate on the role of IIA string theory/M theory and the Dijkgraaf-Vafa matrix model, though integrable models and microscopic instanton calculations are also of considerable importance in this subject.

Level-rank duality of untwisted and twisted D-branes of WZW models is explored. We derive the relation between D0-brane charges of level-rank dual untwisted D-branes of su(N)_K and sp(n)_k, and of level-rank dual twisted D-branes of su(2n+1)_2k+1. The analysis of level-rank duality of twisted D-branes of su(2n+1)_2k+1 is facilitated by their close relation to untwisted D-branes of sp(n)_k. We also demonstrate level-rank duality of the spectrum of an open string stretched between untwisted or twisted D-branes in each of these cases., Comment: 20 pages. v2: minor clarification and added references

We present a matrix-model expression for the sum of instanton contributions to the prepotential of an N=2 supersymmetric U(N) gauge theory, with matter in various representations. This expression is derived by combining the renormalization-group approach to the gauge theory prepotential with matrix-model methods. This result can be evaluated order-by-order in matrix-model perturbation theory to obtain the instanton corrections to the prepotential. We also show, using this expression, that the one-instanton prepotential assumes a universal form., 20 pages, LaTeX, 2 figures

An exact fully-localized extremal supergravity solution for N_2 D2 branes and N_6 D6 branes, which is dual to 3-dimensional supersymmetric SU(N_2) gauge theory with N_6 fundamentals, was found by Cherkis and Hashimoto. In order to consider the thermal properties of the gauge theory we present the non-extremal extension of this solution to first order in an expansion near the core of the D6 branes. We compute the Hawking temperature and the black brane horizon area/entropy. The leading order entropy, which is proportional to N_2^{3/2} N_6^{1/2} T_H^2, is not corrected to first order in the expansion. This result is consistent with the analogous weak-coupling result at the correspondence point N_2 ~ N_6., Comment: 14 pages

We study the matrix model/gauge theory connection for three different N=1 models: U(N) x U(N) with matter in bifundamental representations, U(N) with matter in the symmetric representation, and U(N) with matter in the antisymmetric representation. Using Ward identities, we explicitly show that the loop equations of the matrix models lead to cubic algebraic curves. We then establish the equivalence of the matrix model and gauge theory descriptions in two ways. First, we derive generalized Konishi anomaly equations in the gauge theories, showing that they are identical to the matrix-model equations. Second, we use a perturbative superspace analysis to establish the relation between the gauge theories and the matrix models. We find that the gauge coupling matrix for U(N) with matter in the symmetric or antisymmetric representations is_not_ given by the second derivative of the matrix-model free energy. However, the matrix-model prescription can be modified to give the gauge coupling matrix., 27 pages, 2 figures; v2: minor corrections and clarifications; v3: published version

We study the pp-wave limits of various elliptic models with orientifold planes and D7-branes, as well as the pp-wave limit of an orientifold of adS_5 x T^{11}. Many of the limits contain both open and closed strings. We also present pp-wave limits of theories which give rise to a compact null direction and contain open strings. Maps between the string theory states and gauge theory operators are proposed., 33 pages, no figures, LaTeX. v2: reference fixed

We study the N=1 Sp(2N+2M)xSp(2N) gauge theory on a stack of N physical and M fractional D3-branes in the background of an orientifolded conifold. The gravity dual is a type IIB orientifold of adS_5xT^11 (with certain background fluxes turned on) containing an O7-plane and 8 D7-branes. In the conformal case (M=0), we argue that the alpha'^2-corrections localized on the 8 D7-branes and the O7-plane should give vanishing contributions to the supergravity equations of motion for the bulk fields. In the cascading case (M not equal to 0), we argue that the alpha'^2-terms give rise to corrections which in the dual Sp(2N+2M)xSp(2N) gauge theory can be interpreted as corrections to the anomalous dimensions of the matter fields., Comment: 28 pages, 3 figures, LaTeX; v2: references added; v3: minor changes

We analyze the large N supergravity descriptions of the class of type IIB models T-dual to elliptic type IIA brane configurations containing two orientifold 6-planes and up to two NS 5-branes. The T-dual IIB configurations contain N D3-branes in the background of an orientifold 7-plane and, in some models, a Z_2 orbifold and/or D7-branes, which give rise to four-dimensional N=2 (or N=4) gauge theories with at most two factors. We identify the chiral primary states of the supergravity theories, and match them to gauge invariant operators of the corresponding superconformal theories using Maldacena's duality., Comment: 44 pages (typo corrected)