Quantum Fields and Strings

Non-relativistic versions of the AdS/CFT conjecture have recently been investigated in some detail. These have primarily been in the context of the Schrodinger symmetry group. Here we talk of a study based on a different non-relativistic conformal symmetry: one obtained by a parametric contraction of the relativistic conformal group. The resulting Galilean conformal symmetry has the same number of generators as the relativistic symmetry group and thus is different from the Schrodinger group (which has fewer). One of the interesting features of the Galilean Conformal Algebra is that it admits an extension to an infinite dimensional symmetry algebra (which can potentially be dynamically realised). The latter contains a Virasoro-Kac-Moody subalgebra. We comment on realisations of this extended symmetry in a boundary field theory. We also propose a somewhat unusual geometric structure for the bulk gravity dual to any realisation of this symmetry. This involves taking a Newton-Cartan like limit of Einstein's equations in anti de Sitter space which singles out an $AdS_2$ comprising of the time and radial direction. The infinite dimensional Virasoro extension is identified with the asymptotic isometries of this $AdS_2$.

It has been conjectured that higher-dimensional rotating black holes become unstable at a sufficiently large value of the rotation, and that new black holes with pinched horizons appear at the threshold of the instability. We search numerically, and find, the stationary axisymmetric perturbations of Myers-Perry black holes with a single spin that mark the onset of the instability and the appearance of the new black hole phases. We also find new ultraspinning Gregory-Laflamme instabilities of rotating black strings and branes.

I will survey some open problems posed by experiments on condensed matter systems, such as the high temperature superconductors. I will argue that their solutions require analyses of strong-coupling regimes which cannot be addressed by conventional field-theoretic means. I will describe insights drawn from the AdS/CFT correspondence, and discuss the connections to theories with simple gravity duals.

Ultrarelativistic heavy-ion collisions are one of the most difficult problems for theoretical physicists: they probe non-abelian dynamics deep in the non-perturbative (strong coupling) regime in a many-body system, are highly dynamical (strong gradients), exhibit collective behavior, and involve phase transitions. Fluid dynamics with input from holography is surprisingly good at describing some aspects of experimental data in heavy-ion collisions. I will review some of this successful description, its limitations, and point out open problems that one may be able to understand using gauge/gravity duality.

We utilize the tools of the gauge/gravity correspondence in order to investigate electroweak symmetry breaking (EWSB). For quite some time now, a walking technicolor sector has been viewed by phenomenologists as a very promising alternative to the Higgs boson. Unfortunately however, no precise computations have been possible since in the technicolor gauge theory EWSB is due to strong-coupling dynamics. Using recent developments in the gauge/gravity duality, we construct a gravity dual of a walking technicolor model and aim to compute the Peskin-Takeuchi S-parameter, which is an observable that can distinguish between a Higgs and a technicolor sector.

Recently there has been great interest in calculating transport coefficients for field theories at large coupling, using AdS/CFT. In this talk I will discuss recent work showing how to use the membrane paradigm to easily compute the shear viscosity and conductivity in arbitrary gravity theories. In a certain sense these can be thought of as effective couplings at the black hole horizon dual to the field theory plasma. An explicit Wald-like formula for these couplings is given for a large class of generalized gravity theories.

Complete classification of topological insulators (including, e.g., the quantum Hall effect and the quantum spin Hall systems), and superconductors (including, e.g., chiral p-wave SC and the B-phase of 3He). An interacting bosonic model that realizes a topological superconducting phase in three spatial dimensions.

We study the sub-structure of heterotic Kahler moduli space due to the presence of non-Abelian internal gauge fields from the perspective of the four-dimensional effective theory. Internal gauge fields can be supersymmetric in some regions of Kahler moduli space but break supersymmetry in others. In the context of the four-dimensional theory, we investigate what happens when the Kahler moduli are changed from the supersymmetric to the non-supersymmetric region. Our results provide a low-energy description of supersymmetry breaking by internal gauge fields as well as a physical picture for the mathematical notion of bundle stability. Specifically, we find that at the transition between the two regions an additional anomalous U(1) symmetry appears under which some of the states in the low-energy theory acquire charges. We compute the associated D-term contribution to the four-dimensional potential which contains a Kahler modulus dependent Fayet-Iliopoulos term and contributions from the charged states. We show that this Dterm correctly reproduces the expected physics. Several mathematical conclusions concerning vector bundle stability are drawn from our arguments. We also discuss possible physical applications of our results to heterotic model building and moduli stabilisation.

We present a string dual to finite temperature N=4 SYM coupled to Nf massless flavors with abelian symmetry. The solution includes the backreaction of the flavor up to second order in the ratio N_f/N_c times the 't Hooft coupling at the temperature of the dual QGP. The thermodynamics show a departure from conformality as a second order effect, and the energy loss of a quark through the plasma is enhanced by new degrees of freedom.