We revisit the singular IIB supergravity solution describing M fractional 3branes on the conifold [hep-th/0002159]. Its 5-form flux decreases, which we explain by showing that the relevant N = 1 SUSY SU (N +M )×SU (N ) gauge theory undergoes repeated Seiberg-duality transformations in which N → N − M . Far in the IR the gauge theory confines; its chiral symmetry breaking removes the singularity of hep-th/0002159 by deforming the conifold. We propose a non-singular pure-supergravity background dual to the field theory on all scales, with small curvature everywhere if the 't Hooft coupling g s M is large. In the UV it approaches that of hep-th/0002159, incorporating the logarithmic flow of couplings. In the IR the deformation of the conifold gives a geometrical realization of chiral symmetry breaking and confinement. We suggest that pure N = 1 Yang-Mills may be dual to strings propagating at small g s M on a warped deformed conifold. We note also that the standard model itself may lie at the base of a duality cascade.

We show that manifolds of fixed points, which are generated by exactly marginal operators, are common in N=1 supersymmetric gauge theory. We present a unified and simple prescription for identifying these operators, using tools similar to those employed in two-dimensional N=2 supersymmetry. In particular we rely on the work of Shifman and Vainshtein relating the β-function of the gauge coupling to the anomalous dimensions of the matter fields. Finite N=1 models, which have marginal operators at zero coupling, are easily identified using our approach. The method can also be employed to find manifolds of fixed points which do not include the free theory; these are seen in certain models with product gauge groups and in many non-renormalizable effective theories. For a number of our models, S-duality may have interesting implications. Using the fact that relevant perturbations often cause one manifold of fixed points to flow to another, we propose a specific mechanism through which the N=1 duality discovered by Seiberg could be associated with the duality of finite N=2 models.

We consider general aspects of N = 2 gauge theories in three dimensions, including their multiplet structure, anomalies and non-renormalization theorems. For U (1) gauge theories, we discuss the quantum corrections to the moduli space, and their relation to "mirror symmetries" of 3d N = 4 theories. Mirror symmetry is given an interpretation in terms of vortices. For SU (N c ) gauge groups with N f fundamental flavors, we show that, depending on the number of flavors, there are quantum moduli spaces of vacua with various phenomena near the origin.3/97 * On leave

We consider high-energy fixed-angle scattering of glueballs in confining gauge theories that have supergravity duals. Although the effective description is in terms of the scattering of strings, we find that the amplitudes are hard (power law). This is a consequence of the warped geometry of the dual theory, which has the effect that in an inertial frame the string process is never in the soft regime. At small angle we find hard and Regge behaviors in different kinematic regions.The idea that large-N QCD can be recast as a string theory has been a tantalizing goal since the original proposal of 't Hooft [1]. At low energy, strings give a natural representation of confinement, but the high energy behavior has always presented a fundamental challenge: gauge theory amplitudes are hard, while string theory amplitudes are soft. Thus, the ordinary critical string theory must be modified.This subject has taken an interesting turn with Maldacena duality [2,3]. The original duality was for conformal theories, but various perturbations produce gauge/string duals with a mass gap, confinement, and chiral symmetry breaking [4][5][6][7]. While these theories have QCD-like behavior at low energy, they also differ from QCD at high energy. They are not asymptotically free; rather, the 't Hooft coupling must remain large at all energies in order to obtain a useful string dual. Still, as QCD is itself a nearly-conformal field theory at high energies, many of their qualitative features should be similar.In this paper we will address the following puzzle: in these theories, hadronic amplitudes are well-described at large 't Hooft parameter as the scattering of strings, for which the high energy behavior is soft. How does the dual string theory generate the hard behavior of the gauge theory?Let us first explain the amplitudes to be considered. Conformal field theories, the subject of the original Maldacena duality, do not have an S-matrix. (There has been some discussion of the ten-dimensional S-matrix of the dual string theory, and its representation in terms of gauge theory correlators [8].) However, once conformal symmetry is broken and a mass gap produced, the theory has an ordinary four-dimensional S-matrix. We will then study the 2 → m scattering of closed strings, corresponding to exclusive glueball scattering, at large energy √ s and fixed angles. There is a simple dimensional prediction for exclusive amplitudes of low-lying hadrons in * Institute for Theoretical Physics, University of California, Santa Barbara CA 93106-4030 † Dept. of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19146 QCD [9,10] and other asymptotically free confining theories: they scale aswhere the sum runs over all initial and final hadrons, and n i is the minimum number of hard constituents in the i th hadron. Importantly, n i is also the twist τ i (dimension minus spin) of the lowest-twist operator that can create the ith hadron: the interpolating fermion and gauge field strength operators (and scalars, if present) each have minim...

Abstract:The traditional description of high-energy small-angle scattering in QCD has two components -a soft Pomeron Regge pole for the tensor glueball, and a hard BFKL Pomeron in leading order at weak coupling. On the basis of gauge/string duality, we present a coherent treatment of the Pomeron. In large-N QCD-like theories, we use curved-space string-theory to describe simultaneously both the BFKL regime and the classic Regge regime. The problem reduces to finding the spectrum of a single j-plane Schrödinger operator. For ultraviolet-conformal theories, the spectrum exhibits a set of Regge trajectories at positive t, and a leading j-plane cut for negative t, the cross-over point being model-dependent. For theories with logarithmicallyrunning couplings, one instead finds a discrete spectrum of poles at all t, where the Regge trajectories at positive t continuously become a set of slowly-varying and closely-spaced poles at negative t. Our results agree with expectations for the BFKL Pomeron at negative t, and with the expected glueball spectrum at positive t, but provide a framework in which they are unified. Effects beyond the single Pomeron exchange are briefly discussed.

We consider examples of "hidden-valley" models, in which a new confining gauge group is added to the standard model. Such models often arise in string constructions, and elsewhere. The resulting (electrically-neutral) bound states can have low masses and long lifetimes, and could be observed at the LHC and Tevatron. Production multiplicities are often large. Final states with heavy flavor are common; lepton pairs, displaced vertices and/or missing energy are possible. Accounting for LEP constraints, we find LHC production cross-sections typically in the 1-100 fb range, though they can be larger. It is possible the Higgs boson could be discovered at the Tevatron through rare decays to the new particles.

We study deep inelastic scattering in gauge theories which have dual string descriptions. As a function of gN we find a transition. For small gN , the dominant operators in the OPE are the usual ones, of approximate twist two, corresponding to scattering from weakly interacting partons. For large gN , double-trace operators dominate, corresponding to scattering from entire hadrons (either the original 'valence' hadron or part of a hadron cloud.) At large gN we calculate the structure functions. As a function of Bjorken x there are three regimes: x of order one, where the scattering produces only supergravity states; x small, where excited strings are produced; and, x exponentially small, where the excited strings are comparable in size to the AdS space. The last regime requires in principle a full string calculation in curved spacetime, but the effect of string growth can be simply obtained from the world-sheet renormalization group.

In this paper the connection between standard perturbation theory techniques and the new Bern-Kosower calculational rules for gauge theory is clarified. For oneloop effective actions of scalars, Dirac spinors, and vector bosons in a background gauge field, Bern-Kosower-type rules are derived without the use of either string theory or Feynman diagrams. The effective action is written as a one-dimensional path integral, which can be calculated to any order in the gauge coupling; evaluation leads to Feynman parameter integrals directly, bypassing the usual algebra required from Feynman diagrams, and leading to compact and organized expressions. This formalism is valid off-shell, is explicitly gauge invariant, and can be extended to a number of other field theories.