Inspired by the multiplicative nature of the Ramanujan modular discriminant, Delta, we consider physical realizations of certain multiplicative products over the Dedekind eta-function in two parallel directions: the generating function of BPS states in certain heterotic orbifolds and elliptic K3 surfaces associated to congruence subgroups of the modular group. We show that they are, after string duality to type II, the same K3 surfaces admitting Nikulin automorphisms. In due course, we will present some identities arising from q-expansions as well as relations to the sporadic Mathieu group M24.

Motivated by either condensed matter or quantum gravity holographic considerations, I will discuss some preliminary work on how to compute the time evolution in Renyi entropies in 2d CFTs in the large c limit for thermal states perturbed by localized primary operators. Time permitting, I will comment on the potential relation between this work and previous holographic calculations in the context of the EPR=ER conjecture.

Is there a consistent patching for double manifolds? I shall demonstrate that the solution of the strong section condition leads to exact 3-form field strengths. I shall also prove that the consistency of the examples presented so far depends on the choice of the atlas, and so they are not general covariant. Then I shall suggest a new construction which resolves some of the puzzles and possibly specifies the appropriate spaces up to homotopy.

We classify the possible linear unfolded equations for propagating bosonic higher-spin tensor fields in AdS_3 backgrounds. Doing this we reproduce the existing topologically massive and new topologically massive (higher)-spin systems whose content we clarify. We find systems that generalise various critical gravities to higher-spins.

We discuss entanglement and Renyi entropies in two-dimensional conformal field theories with extended symmetry algebras of W-type, in the semiclassical (large-c) limit. From the CFT perspective, the computation of these non-local observables involves the study of semiclassical conformal blocks in theories with additional conserved currents beyond the stress tensor. From an AdS perspective, the problem can be tackled using recent holographic proposals in terms of Wilson lines in the dual three-dimensional higher spin theories. We discuss non-trivial examples exhibiting the agreement between bulk and boundary computations.

I discuss the quantization of a perfect fluid. This differs from textbook QFT, because of the presence of vortex modes, which map to an infinite collection of quantum mechanical free particles rather than harmonic oscillators. As a result, there is no Fock space and no S-matrix. I argue that there exists, nevertheless, a consistent effective field theory description, valid at large distances and times.

Galaxy clusters are the most efficient convertors of axion-like particles to photons in the universe. I discuss the physics and phenomenology of ALPs, and describe their astrophysical implications, with particular reference to the recently observed 3.5 keV X-ray line that is a candidate for a dark matter decay line.

F-theory paints a beautiful picture that relates gauge theories to purely geometric information, whereby the Dynkin diagrams of gauge groups come to life as 2-cycles of internal spaces. The caveat is that, such spaces are necessarily singular, and treating them sensibly requires resolving or deforming the singularities. Recently, my collaborator R. Savelli and I have proposed a new strategy that allows one to deal with singular spaces directly. It is based on Eisenbud’s so-called matrix factorisations. This remarkably simple concept has very deep connections to the mathematics of singularities. In this talk, I will review the basic notions needed to formulate the issues, assuming only standard knowledge of string theory. Then, after introducing our proposal, I will show examples of its applications, such as computations of chiral spectra for bound states of 7-branes.

Light-like polygonal super-Wilson loops are dual to scattering amplitudes in planar N=4 super-Yang-Mills and enjoy an infinite-dimensional Yangian symmetry which extends the superconformal symmetry.  However, this symmetry is anomalous.  In this talk we will describe a super-Wilson loop on a smooth contour, which is free of UV divergences and on which the superconformal symmetry operators are not anomalous.  We also study the action of level one Yangian generators on the one-loop expectation value of this super-Wilson loop. [This is work in progress with N.Beisert, D.Muller and J.Plefka]

CFTs at large central charge display some universal features which can be inferred from holography. Using these as a guide one can obtain some necessary conditions for a given CFT to admit a classical gravity dual. I will describe attempts to construct a large class of CFTs satisfying these conditions exploiting some technology of permutation orbifolds. Time permitting I will also outline some tests for the sufficiency of these conditions.

The algebras of higher spin symmetries in conformal field theories in four and six dimensions are not unique and have a richer structure due to the existence of infinite short multiplets besides the usual scalar and spinor. We will focus on recent results that show there exists a one parameter family (continuous of d=4 and discrete for d=6) of higher spin algebras and superalgebras, and give an explicit unitary representation for these algebras using quasiconformal methods. We will also discuss the implications of these results for the AdS5/CFT4 and AdS7/CFT6 higher spin holography.

I will explain how to compute the Hilbert series that counts chiral operators parametrising the Coulomb branch of the moduli space of vacua of three-dimensional N=4 supersymmetric gauge theories. The formula has applications to Physics, such as to the study of infrared dualities in three dimensions and of string backgrounds with eight supercharges, as well as to Mathematics, where it provides a new way to characterise HyperKaehler cones as algebraic varieties.  I will then show how the Coulomb branch of certain 3d N=4 generalised quiver gauge theories can be used to compute the Hilbert series of the moduli space of k G-instantons, for any simple Lie group G. The construction is alternative to the ADHM construction that is only available for classical groups G.

TBA

Workshop information and registration http://www.mth.kcl.ac.uk/~ss299/MOST/

Workshop homepage for information and registration http://www.mth.kcl.ac.uk/~ss299/MOST/

I will discuss basic features of a formulation of higher-spin field theory in which conventional space-time gets extended to a hyperspace with a number of extra dimensions that effectively describe the spin degrees of freedom of the fields in the ordinary space-time. In this formulation an infinite number of higher spin fields are packed into a single scalar and spinor field propagating in the hyperspace. The dynamics of higher spin fields is encoded in equations of motion of the scalar and spinor hyperfields. The hyperfield equatons on flat and AdS-like hyperspaces are related to each other by a generalized conformal transformation, which also relates two-, three- and four-point functions in the AdS-like hyperspace to the corresponding correlators in the flat hyperspace.

This is a one-day meeting on localisation and gauge gravity duality. More information at http://kings-meeting.wikidot.com/

South East Mathematical Physics Seminar: For details see http://www.mth.kcl.ac.uk/SEMPS/ Speakers: Leron Borsten,Paul Sutcliffe, Vidas Regelskis, Abera Muhamed, Craig Lawrie

Student Triangle Seminar! http://www.mth.kcl.ac.uk/studenttriangle.html

Recently a powerful approach to the computation of one-point functions in the quantum XXZ spin 1/2 chain has been proposed by Boos, Jimbo, Miwa and Smirnov; this framework relies on the existence of a particular basis in the state space of the theory: the fermionic basis. I will present the construction of these fermions for the scaling limit of inhomogeneous XXZ spin 1/2 chain, the sine-Gordon model, and for its twin, the sinh-Gordon model. If time allows it, I will briefly present a possible interpretation of the fermionic basis and one-point functions in terms of the action of a modified version of the sinh-Gordon model.