Past String Theory Seminar

Abstract: Recent developments in quantum field theory and twistor-string theory have thrown up surprising structures in the perturbative approach to gravity that cry out for a non-perturbative explanation. Firstly the MHV scattering amplitudes, those involving just two left handed and n-2 right handed outgoing gravitons are particularly simple, and a formalism has been proposed that constructs general graviton scattering amplitudes from these MHV amplitudes as building blocks. This formalism is chiral and suggestive of deep links with Ashtekar variables and twistor theory. In this talk, the MHV amplitudes are calculated ab initio by considering scattering of linear gravitons on a fully nonlinear anti-self-dual background using twistor theory, and a twistor action formulation is provided that produces the MHV formalism as its Feynman rules.

Abstract: In this talk, I will give an overview of the new developments in the AdS_4/CFT_3 correspondence. I will present in detail an N=6 Chern-Simons-matter theory with gauge group U(N) x U(N) that is dual to N M2 branes in the orbifold C^4/Z_k. This theory can be derived from a construction involving D3 branes intersecting (p,q) fivebranes. I will also discuss various quantum mechanical aspects of this theory, including an enhancement of its supersymmetry algebra at Chern-Simons levels 1 and 2, and some novel phenomenon that arise in the U(N) x U(M) theory dual to configurations with N-M fractional branes. A generalization to N=3 CSM theories dual to AdS_4 x M_7, where M_7 is a 3-Sasakian 7-manifold, will be explained. The seminar will be based primarily on Aharony, Bergman, DJ, Maldacena; Aharony, Bergman, DJ; DJ, Tomasiello.

Abstract: It is known that many Calabi-Yau manifolds form a connected web. The question of whether all CY manifolds form a single web depends on the degree of singularity that is permitted for the varieties that connect  the distinct families of smooth manifolds. If only conifolds are allowed then, since shrinking two-spheres and three-spheres to points cannot affect the fundamental group, manifolds with different fundamental groups will form disconnected webs. We examine these webs for the tip of the distribution of CY manifolds where the Hodge numbers $(h^{11},h^{21})$ are both small. In the tip of the distribution the quotient manifolds play an important role. We generate via conifold transitions from these quotients a number of new manifolds. These include a manifold with $\chi =-6$, that is an analogue of the $\chi=-6$ manifold found by Yau,  and manifolds with an attractive structure that may prove of interest for string phenomenology.

Abstract: We discuss an extension of Hitchin's generalised geometry, based on the exceptional groups, that provides a unified geometrical description of supersymmetric flux backgrounds in eleven-dimensional supergravity. We focus on N=1 seven-dimensional compactifications. The background is characterised by an element phi, the analogue of the generalised complex structure, that lies in a particular orbit of the 912 representation of E7. As an application we show that the four-dimensional effective superpotential takes a universal form, that is, a homogeneous E7-invariant functional of phi.

Abstract: We discuss recent techniques to compute one-loop amplitudes in QCD and show that all N-gluon one-loop helicity amplitudes can be computed numerically for arbitrary N with an algorithm which has a polynomial growth in N.

Abstract: I will describe how computations are done using "Groebner bases" in quotient rings of polynomial rings, and I will describe explicitly the form of a particular Groebner basis for the ideal defining the ring parametrizing all factorizations of a monic polynomial of degree a+b+...+e into monic factors of degree a,b,...,e. That can be and is used in practice to compute intersection numbers involving of algebraic cycles arising as Chern classes on flag bundles of vector bundles. Simplest example: how many lines in 3-space meet four fixed lines?

Abstract: Different phenomenological scenarios emerging from the exponentially large volume string constructions will be discussed with and without low energy supersymmetry.

Abstract: I will talk about how the reformulation of perturbative Yang-Mills theory in terms of MHV rules accounts for one-loop amplitudes for gluons of the same helicity, and some of the effects of introducing a regulator.

Abstract: Compact $G_2$ manifolds with isolated conical singularities arise naturally in M-theory. I will discuss such manifolds, and explain a method to ``desingularize'' them by glueing in pieces of asymptotically conical $G_2$ manifolds. There are topological obstructions to such desingularizations that depend on the rate of convergence to the cone at the singularities, and on the geometry of the links of the cones. If time permits, I will also briefly discuss a new related project with Dominic Joyce which could provide the first examples of such manifolds, as well as a possible new construction of smooth compact $G_2$ manifolds.

Abstract: We consider deformations of torsion-free $ G_2 $ structures, defined by the $ G_2 $-invariant 3-form $ \phi $ and compute the expansion of the Hodge star of $ \phi $ to fourth order in the deformations of $ \phi $. By considering M-theory compactified on a $ G_2 $ manifold, the $ G_2 $ moduli space is naturally complexified, and we get a Kahler metric on it. Using the expansion of the Hodge star of $ \phi $ we work out the full curvature of this metric and relate it to the Yukawa coupling.

Abstract: We will discuss string $AdS_4$ domain wall solutions with stabilized moduli. These solutions are interesting, since they potentially induce decay processes between different vacua within the string landscape. Moreover, we discuss how black hole physics provide another tool of seeing through the vacuum landscape.

Abstract: We discuss the string-inspired approach to gauge theory amplitudes prompted by the work of Alday and Maldacena, in particular its application to weak coupling.

Abstract: Quantum Hall systems are characterized by a spectacular set of observations (universal low-temperature conductivity, critical behaviour and semi-circle laws for transitions between Quantum Hall states) that are more robust than would be expected from the detailed theory of underlying electron dynamics. The talk starts with a summary of these observations, and their derivation from the assumption that the important charge carriers at the low energies relevant to conductivity measurements are weakly interacting particles or vortices. This implies a large emergent duality symmetry (a level two subgroup of SL(2,Z)), whose presence underlies the robustness of the observations in question. The newly-discovered and unusual Quantum Hall properties of graphene are discussed as providing a new test of this picture.

Abstract: The alternative action for Yang-Mills theory, which Lionel Mason formulated in twistor space, explains some of the simplicities of gluon scattering amplitudes. We will review the derivation of the familiar CSW rules concerning tree-level scattering, show that the `missing' three-point amplitude can be correctly recovered and elucidate the connection with the canonical Lagrangian approach of Mansfied, Morris, et. al.

Abstract: For a large class of compactifications of interest in string phenomenology, the task of finding vacua of the four dimensional effective theories can be rewritten as a simple problem in algebraic geometry. Using recent developments in computer algebra, the task can then be rapidly dealt with in a completely algorithmic fashion. I shall review the main points of hep-th/0606122 and hep-th/0703249 in which this approach to finding vacua was set out, before moving on to a description of the Mathematica package STRINGVACUA (as described in arXiv:0801.1508 [hep-th]). This package uses the power of the computer algebra system Singular and provides a user-friendly implementation of our methods, intended for use by physicists, within the comfortable working environment of Mathematica.

Abstract: I show that the effective action of string compactifications has astructure that can naturally solve the supersymmetric flavour and CP problems. At leading order in the $g_s$ and $\alpha'$ expansions, the hidden sector factorises. The moduli space splits into two mirror parts that depend on K\"ahler and complex structure moduli. Holomorphy implies the flavour structure of the Yukawa couplings arises in only one part. In type IIA string theory flavour arises through the K\"ahler moduli sector and in type IIB flavour arises through the complex structure moduli sector. This factorisation gives a simple solution to the supersymmetric flavour and CP problems: flavour physics is generated in one sector while supersymmetry is broken in the mirror sector. This mechanism does not require the presence of gauge, gaugino or anomaly mediation and is explicitly realised by phenomenological models of IIB flux compactifications.

Abstract: The moduli space of Calabi-Yau manifolds have a natural geometrical structure that has come to be known as special geometry. This geometry will be reviewed in the complex context and it will be shown that much of the structure persists for p-adic Calabi-Yau manifolds.

Abstract: In this talk, I will describe recent work in string phenomenology from the perspective of computational algebraic geometry. I will begin by reviewing some of the long-standing issues in heterotic model building and describe the difficult task of producing realistic particle physics from heterotic string theory. This goal can be approached by creating a large class of heterotic models which can be algorithmically scanned for physical suitability. I will outline a well-defined set of heterotic compactifications over complete intersection Calabi-Yau manifolds using the monad construction of vector bundles. Further, I will describe how a combination of analytic methods and computer algebra can provide efficient techniques for proving stability and calculating particle spectra.

Abstract: The deconfinement transition in gauge theories, in which the Polyakov loop acquires a non-zero expectation value, is described in AdS/CFT as the formation of a black hole in the dual graviational theory. We will explain how to compute the free energy diagram for the Polyakov loop by a constrained gravitational path integral, leading to a new class of black hole solutions.