## Robert Karp : A convex optimization problem in string theory

- String Theory ( 229 Views )For nearly 25 years Calabi-Yau spaces have played a central role in string theory, yet no explicit metric was known. I will outline ideas pioneered by Donaldson and Yau that lead to such metrics numerically; then extend this approach to solving the hermitian Yang-Mills equation, and also obtain metrics on moduli spaces. Knowledge of these quantities is unavoidable for physical predictions.

## Albion Lawrence : Worldsheet RG and target space time evolution

- String Theory ( 33 Views )A useful tool to study tachyon condensation in string theory is the renormalization group flow of the associated relevant perturbation of a conformal field theory. One assumes that the worldsheet RG flow reflects the actual time evolution of the target space. The relationship is not completely direct: for example, the RG equations are first order differential equations, while the target space equations of motion are at least second order in time. To put the correspondence on firmer footing we discuss the coupling of non-conformal 2d field theories with $n\geq 25$ scalar fields to 2d gravity, following previous discussions of Polyakov and of Schmidhuber and Tseytlin. The conformal mode of the metric becomes a timelike target space direction with a Liouville action, so that the Liouville dressing of an operator is related to its scaling properties. We will give a conjecture for the equations of motion for the worldsheet couplings, which reduces to the standard 2d RG equations in the limit that the Liouville mode becomes semiclassical, and describe our current attempts to prove this conjecture.

## Peter Miller : The Zero-Brane as a Soliton

- String Theory ( 33 Views )We present an exact construction of the D0-brane as a soliton on the worldvolume of a BPS D2-brane in the presence of a large B field. We match the mass and spectrum of fluctuations of this soliton to the D0-D2 conformal field theory. This spectrum includes a tachyon: the endpoint of tachyon condensation represents the ``disappearance'' of the D0-brane, and all modes associated with it, as it dissolves in the D2-brane. This construction thus sheds some light on issues related to tachyon condensation.

## David Morrison : Non-Spherical Horizons

- String Theory ( 33 Views )The ``horizon'' of N coincident branes in Minkowski space is the unit sphere in the transverse directions; in a certain scaling limit, string or M-theory in the presence of branes is dual to a compactification on the product of an anti-de Sitter space with the horizon. We study the analogous limit when N branes are placed at a singular point, so that the horizon becomes the so-called ``link'' of the singularity, and is no longer a sphere. A similar scaling argument leads to a natural extension of Maldacena's celebrated ``AdS/CFT correspondence conjecture'' to this situation. The conformal field theories in question have less supersymmetry than the cases studied by Maldacena, with the amount being determined by the Killing spinors on the horizon manifold. An important mathematical tool is the relationship -- derived some years ago by C. Bär -- between Killing spinors on a manifold and covariantly constant spinors on the cone over that manifold.

## David Morrison : Introduction to F-Theory, II

- String Theory ( 32 Views )This is the second of a series of lectures on F-theory. The lectures will present the theory of elliptically fibered Calabi-Yau manifolds in considerable detail, explain how these manifolds are used to produce string vacua by means of the ``F-theory'' construction, and how various properties of these string vacua are determined by the corresponding Calabi-Yau manifolds.

## Washington Taylor : Counting flux vacua with special properties

- String Theory ( 32 Views )I will discuss the statistical analysis of flux vacua with special properties such as (no-scale) supersymmetry and discrete symmetries. Unlike generic flux vacua, enumeration of such special vacua can require number-theoretic methods.

## Lilia Anguelova : R^4 Corrections and Flux Superpotential in Heterotic M-theory

- String Theory ( 31 Views )I will describe two kinds of corrections to the previously known effective action of heterotic M-theory. The first is due to taking into account the 11d R^4 term. This results in a new contribution to the Kahler potential of the four-dimensional effective theory. The second comes from the flux-generated superpotential. To derive systematically the form of this superpotential, one has to use the approach of group structures. It is essential to consider SU(3), not G_2, structure on the internal 7d manifold. Finally, I will address the issue of how these corrections affect the existence of dS vacua in heterotic M-theory, which were originally found by balancing open membrane instanton effects and gaugino condensation.

## Marcel Vonk : Topological Strings, Black Holes and Matrix Models

- String Theory ( 31 Views )It is known that many random matrix models have a dual description in terms of a topological string theory. Moreover, recently, Ooguri, Strominger and Vafa have shown that one can calculate certain properties of N=2 supersymmetric black holes in four dimensions using a topological string theory. In this talk, based on hep-th/0410141, I connect these two developments, and discuss what matrix models can teach us about black holes.

## Ronen Plesser : Conformal Field Theories from Branes at Singularities

- String Theory ( 30 Views )We study the conformal field theory describing the extreme low-energy excitations of parallel D3-branes located at a singular point of the transverse space. For quotient singularities such a description is known. Using the fact that partial resolutions of quotient singularities contain other kinds of singular points, as well as a mapping of the moduli space of a singularity onto the parameter space of the corresponding field theory, we compute the worldvolume field theory for branes at more general singularities. We compare our results to the predictions of an extended version of Maldacena's AdS/CFT correspondence as presented last week by D. Morrison.

## Angel Uranga : Brane Configurations and Branes at Singularities

- String Theory ( 30 Views )The dynamics of D branes moving in certain string theory backgrounds can be used to learn about supersymmetric field theories in several dimensions. In this talk I will center on the realization of four-dimensional N=2 and N=1 gauge field theories, by using two types of backgrounds. The first (`brane configurations') involves D branes in the presence of NS fivebranes, whereas the second involves D branes sitting at singular points. A wide variety of conformal theories with marginal couplings, and of finite N=1 theories arises from these constructions. I will also emphasize the equivalence of different constructions by T duality.

## David Morrison : Introduction to F-Theory, VI

- String Theory ( 29 Views )This is the sixth of a series of lectures on F-theory. The lectures will present the theory of elliptically fibered Calabi-Yau manifolds in considerable detail, explain how these manifolds are used to produce string vacua by means of the ``F-theory'' construction, and how various properties of these string vacua are determined by the corresponding Calabi-Yau manifolds.

## Paul Frampton : Conformality and String Phenomenology

- String Theory ( 28 Views )(1) After a general description of quiver gauge theories (QGT) which may possess 4-dimensional conformal invariance and which arise from orbifolded AdS/CFT some successful comparisons to the nonsupersymmetric Minimal Standard Model (MSM) are made. (2) A QGT scheme where grand unification of the MSM occurs at about 4 TeV is discussed. This has consequences for the next big collider, the Large Hadron Collider at CERN. (3) It is explained how nonsupersymmetric QGT can subsume an MSM which has no quadratic divergence in its Higgs scalar propagator. The necessary and sufficient condition for such naturalness is that the progenitor QGT possess chiral fermions.

## Sergei Gukov : Warped Compactifications on Calabi-Yau Fourfolds

- String Theory ( 28 Views )Motivated by phenomenological applications we consider (warped) compactifications of type IIA string theory on Calabi-Yau fourfolds in the presence of Ramond-Ramond fluxes. The main goal of the talk is a description of low-energy physics, including a new superspace formulation of two-dimensional N = (2,2) dilaton supergravity coupled to matter, and computation of the effective superpotentials induced by fluxes.

## Igor Klebanov : N=1 Gauge Theory and Warped Deformed Conifold

- String Theory ( 28 Views )We revisit the singular IIB supergravity solution describing M fractional 3-branes 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) x 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 removed 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.

## David Morrison : A New Perspective on Calabi-Yau Geometry, II

- String Theory ( 28 Views )Work over the past few years by Mark Gross, Ilya Zharkov, and Wei-Dong Ruan has led to a clear conjectural picture for the structure of generic supersymmetric T^3 fibrations on Calabi-Yau threefolds. We will explain this picture, show how mirror symmetry would be a natural consequence of it, and discuss other possible applications.

## Mohammad Edalati : On singular effective superpotentials in supersymmetric gauge theories

- String Theory ( 27 Views )Using the generalized Konishi anomaly equation in the chiral ring of a four dimensional N=1 SU(N) supersymmetric gauge theory with fundamental and anti-fundamental matters, we derive the large N_f effective superpotentials of the theory. These superpotentials are singular when expressed in terms of local gauge-invariant chiral fields. We show that these effective superpotentials, despite being singular, are perfectly sensible, i.e. they correctly describe the moduli space of vacua, are consistent under RG flow to fewer flavors upon turning on masses, and also (in the case of SU(2) gauge group) reproduce by a tree-level calculation all the higher-derivative F-terms recently calculated by Beasley and Witten by instanton methods.

## Jeff Harvey : D-Branes and Asymmetric Orbifolds

- String Theory ( 27 Views )D-branes are usually treated as classical geometric objects in string theory. They can be defined more abstractly in conformal field theory using the boundary state formalism. Some general issues involving this formalism will be discussed and illustrated with examples involving D-branes on both symmetric and asymmetric orbifolds.

## Albion Lawrence : Low-Energy Physics of Warped Compactifications

- String Theory ( 27 Views )A large class of string compactifications are warped products of the compactification manifold and our four-dimensional spacetime, where the spacetime metric depends on the position in the compactification manifold. New, calculable regimes will arise when warp factors are large and when several different regions with interesting physics are spatially separated in the compactification manifold. We discuss a variant of the Randall-Sundrum scenario which, at low energies, captures the essential features of this regime. We discuss the low-energy effective theory of such a scenario, including the important scales and leading irrelevant operators. We comment critically on the conjectured relationship between the Randall-Sundrum proposal and the AdS/CFT correspondence. Finally, we discuss some phenomenological consequences of these models: namely, a new mediation mechanism for supersymmetry breaking, and a dark matter candidate which might explain some puzzles in the structure of galactic dark matter halos.

## Nikita Nekrasov : Four-Manifolds, Symplectic Geometry, and Mirror Symmetry

- String Theory ( 27 Views )Some of the old problems in algebraic geometry, as well as relatively new problems in the theory of quantization, were solved using topological sigma models. The sigma models describe maps of a manifold *M* to a target space *X*. It is very well-known that no sensible theory exists when the dimension of *M* is greater than two. In my talk I will try to argue in favor of the existence of an interesting theory of maps in the case where *M* is a four-dimensional Riemannian manifold and *X* is a classifying space of some compact Lie group (or its finite-dimensional model). To get there we will need to introduce & develop certain aspects of Donaldson theory and higher-dimensional analogues of Whitman hierarchies. No knowledge of Donaldson theory or Whitman hierarchies is necessary.

## Eva Silverstein : Small N 2D Gauge Theory and Small N Supersymmetry

- String Theory ( 27 Views )We discuss aspects of the renormalization group flow of quiver gauge theories in two dimensions, with little or no supersymmetry, in the spirit of earlier work of Zamolodchikov on non-supersymmetric Landau-Ginzburg theory. By using a variety of techniques including analysis of chiral symmetries, identification of operators, and analysis of perturbative gauge theory diagrams, we show that these theories can (at least) be fine-tuned to flow to orbifold conformal field theory in the infrared. This provides a linear sigma model description of string backgrounds with no spacetime supersymmetry, whose applications and limitations we begin to explore.

## Vijay Balasubramanian : Five Dimensions from Four: On Dimensional Transmogrification

- String Theory ( 26 Views )Recent developments have suggested that the classical physics of gravity in a given number of dimensions can be related to a non-gravitational theory in a lower number of dimensions. I will argue that the radial direction of five-dimensional AdS space can be generated by renormalization group (RG) flow from a dual four-dimensional theory. First, I will show that integrating out the physics outside finite balls in AdS spacetime generates a family of actions that satisfies an RG-like equation. Next, I will argue that the trace of the AdS spacetime stress tensor contains analogues of field theory beta functions and gives a gravitational analogue of an RG equation. Turning things around, I will show that the conformal anomaly computed from the four-dimensional field theory dual to AdS space completely encodes the gravitational physics of the skin of the five-dimensional spacetime. Finally, I will argue that recovering the deep interior of the five-dimensional spacetime from the four-dimensional field theory will require exotic new approaches to the renormalization group.