John Voight : On Moduli of Nondegenerate Curves
- String Theory ( 244 Views )We study the conditions under which an algebraic curve can be modelled by a Laurent polynomial that is nondegenerate with respect to its Newton polytope. Such nondegenerate polynomials have become popular objects in explicit algebraic geometry, owing to their connection with toric geometry; however, despite their ubiquity, the intrinsic property of nondegeneracy has not seen much detailed study. We prove that every curve of genus $g \geq 4$ over an algebraically closed field is nondegenerate in the above sense. More generally, let $\mathcal{M}_g^{\textup{nd}}$ be the locus of nondegenerate curves inside the moduli space of curves of genus $g \geq 2$. Then we show that $\dim \mathcal{M}_g^{\textup{nd}} = \min(2g+1,3g-3)$, except for $g=7$ where $\dim \mathcal{M}_7^{\textup{nd}} = 16$; thus, a generic curve of genus $g$ is nondegenerate if and only if $g \geq 4$
Anja Sturm : Coexistence and convergence for voter model with selection
- String Theory ( 238 Views )We consider variations of the usual voter model, which favor types that are locally less common. Such voter models with selection are dual to systems of branching annihilating random walks that are parity preserving. We consider coexistence of types in the voter models which is related to the survival of particles in the branching annihilating random walk. We find conditions for the uniqueness of a homogeneous coexisting invariant law as well as for convergence to this law from homogeneous and coexisting initial laws. For a particular one dimensional model we also show a complete convergence result for any initial condition. This is based on comparison with oriented percolation of the associated branching annihilating random walk.
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.
Mark Jackson : Superstring Cosmology: New Physics in the Sky
- String Theory ( 222 Views )Striking advances in observational cosmology over the past two decades have ushered in a golden era in cosmology, where our focus has turned from what the universe is made of to why it has the form we observe. The leading theory capable of answering such a question, Superstring Theory, does not appear capable of being tested using conventional accelerator-based experiments, forcing us to be more creative in our goal to verify or dismiss it. Focusing on brane inflation as a string theory-inspired model of inflationary cosmology, I will review how the cosmic microwave background (CMB) will provide a deluge of high- precision data into otherwise inaccessible energy scales. These data include possible "Transplanckian" signatures in the power spectrum, indications of variable sound speed or extra dimensions in non- Gaussianity, or constraining the inflation model parameter space using polarization. I then describe how the production of cosmic (super)strings in brane inflation would provide an additional means to verify superstring theory, and which would yield much detailed information about the underlying theory parameters.
Bobby Acharya : M Theory, G_2 Holonomy spaces and N=1 Theories in Four Dimensions
- String Theory ( 42 Views )After reviewing some reasons why one might be interested in G_2 holonomy compactifications of M theory, I shall review some of the recent results about such vacua, which are mainly due to Atiyah, Maldacena, Vafa, Witten, and myself in various collaborations. Topics covered will mainly center around how various aspects of super Yang-Mills theory can be related to properties of M theory in such spacetime backgrounds. These will include instantons, domain walls and confinement.
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 : 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.
David Morrison : Introduction to F-Theory, V
- String Theory ( 32 Views )This is the fifth 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.
Ilarion Melnikov : The Coulomb Branch in Gauged Linear Sigma Models
- String Theory ( 32 Views )I will present recent work with M.R. Plesser on the GLSM perspective on closed string tachyon condensation in non-supersymmetric orbifolds. These models are distinguished from their supersymmetric relatives by the appearance of weakly coupled Coulomb vacua in certain phases of the GLSM. We study the form of A-twisted correlators in these theories. Using standard techniques, we are able to compute these correlators in a pure Higgs phase (one without Coulomb vacua). These correlators are independent of which phase is used to compute them, and thus we can learn about the properties of the Coulomb branch, where direct computations are difficult.
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.
Ronen Plesser : `Toric duality is Seiberg duality
- String Theory ( 31 Views )We study four N=1 SU(N)^6 gauge theories, with bi-fundamental chiral matter and a superpotential. In the infrared, these gauge theories all realize the low-energy world-volume description of N coincident D3-branes transverse to the complex cone over a del Pezzo surface dP_3 which is the blowup of P^2 at three generic points. Therefore, the four gauge theories are expected to fall into the same universality class--an example of a phenomenon that has been termed "toric duality." However, little independent evidence has been given that such theories are infrared-equivalent. In fact, we show that the four gauge theories are related by the N=1 duality of Seiberg, vindicating this expectation. We also study holographic aspects of these gauge theories. In particular we relate the spectrum of chiral operators in the gauge theories to wrapped D3-brane states in the AdS dual description. We finally demonstrate that the other known examples of toric duality are related by N=1 duality, a fact which we conjecture holds generally.
Duiliu-Emanuel Diaconescu : M theory and twisted K theory
- String Theory ( 30 Views )The talk will be focused on the relation between K theory and M theory and it's generalization to nonzero $B$ field. The main idea is a comparison of the long distance partition functions of the two theories. In the process we will outline a derivation of the (twisted) Atiyah - Hirzebruch spectral sequence from M theory. We will also discuss the relation between $SL(2,Z)$ duality and K theory.
Andy Neitzke : Elements of Topological M-Theory
- String Theory ( 30 Views )I will discuss some action functionals constructed by Hitchin which lead to manifolds of special holonomy in six and seven dimensions, and explain how these actions could be related to a topological version of M-theory which deals with variations of G2 structures.
Eric Sharpe : Kähler Cone Substructure
- String Theory ( 30 Views )To define a consistent perturbative geometric heterotic compactification one must specify not only a Calabi-Yau manifold M but also a bundle E on M. The bundle E is required to satisfy a subtle constraint known as ``stability,'' which depends upon the Kähler form. This dependence upon the Kähler form is highly nontrivial---the Kähler cone splits into subcones, with a distinct moduli space of bundles in each subcone---and has long been overlooked by physicists. In this talk we shall describe this behavior and its physical manifestation.
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.
Eva Silverstein : An Approach to Tachyon Dynamics in Closed String Theory
- String Theory ( 29 Views )The talk will begin with a review of some recent progress in non-supersymmetric string theory, motivating a careful study of such backgrounds. Many non-supersymmetric closed string theories have negative modes (``tachyons''). I will describe an approach to understanding the result of tachyon condensation using configurations in string theory of effectively negative but finite tension (such as orientifold planes and their S-duals).
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.
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.