The talk will describe my first interaction with Tom Kibble, when I visited Imperial College in 1961-2; Tom's ground-breaking work on broken symmetry and the Higgs boson; and how a 1967 paper by Tom laid the foundation for understanding the photon. [Symmetry and Fundamental Physics - Tom Kibble at 80]

We will explain the notion of T-duality in supergravity backgrounds with non-Abelian isometries and non-vanishing RR fluxes. We will then focus on type-II backgrounds on which the duality action preserves supersymmetry. For the case of D3-branes at the tip of the conifold dualising along an SU(2) isometry provides a type-IIA background with M-theory lift is of the type describing duals to certain N=1 SCFT quivers produced by M5-branes wrapping a Riemann surface. In the non-conformal cases we find smooth duals in massive IIA supergravity with a Romans mass naturally quantised. We initiate the interpretation of these geometries in the context of the AdS/CFT correspondence and discuss the fate of various charges under dualisation. The backgrounds suggest a form of Seiberg duality in the dual field theories which also exhibit domain walls and confinement in the infrared.

I will present the exact computation of the two-dimensional supersymmetric theories on two-sphere using the localization techniques. I will then apply these new results to study type II string compactifications (with emphasis on the exact Kaehler potential of quantum Kaehler moduli of Calabi-Yau geometry and mirror symmetry) and non-rational CFTs.

I shall discuss the structure of supersymmetry invariants in N=4 supergravity coupled to n vector multiplets, and in particular their transformation properties with respect to duality symmetry. This will permit to discuss the anomalous Ward identities for the duality symmetry, and their consequences on the logarithmic divergences of the theory.

In the first part of my talk, I will present a general classification of Riemannian three-manifolds on which one can put 3d N=2 supersymmetric field theories while preserving some amount of supersymmetry. This formalism clarifies the relationship between the extra couplings necessary to preserve supersymmetry in curved space, on the one hand, and various operators of the flat space theory, on the other hand. In the second part of the talk I will present some simple applications of this formalism. In particular I will present exact results for various two-point functions of N=2 SCFTs which were hitherto out of reach.

I will present a series of new results on classical and quantum properties of maximal supergravity in 4 dimensions, emphasizing the role of the recently discovered "new SO(8) theories". I will explain how this changes our understanding of some general properties of supergravity theories and comment on the impact of these results on the gauge/gravity correspondence.

We study N=2 ADE quiver gauge theories in presence of a non-trivial Omega background along a two dimensional plane. In particular we perform a saddle point analysis to the partition function and derive an epsilon-deformed version of Seiberg-Witten like equations. The result can be interpreted as a non-commutative version of the standard Seiberg-Witten curves associated to the quiver theories.

In recent years there has ben considerable interest in using holographic methods to model strongly interacting condensed matter systems, including unconventional superconductors. However, many high Tc superconductors exhibit d-wave pairing and a satisfactory holographic realization of d-wave superconductors has been elusive. In this talk we will present a top down model for d-wave superconductors and discuss its phenomenology.

A class of non-semisimple extensions of Lie superalgebras is studied. They are obtained by adjoining to the superalgebra its adjoint representation as an abelian ideal. When the superalgebra is of affine Kac-Moody type, a generalisation of Sugawara’s construction is shown to give rise to a copy of the Virasoro algebra and so, presumably, to a conformal field theory. Evidence for this is detailed for the extension of the affinisation of the superalgebra gl (1|1): Its highest weight irreducible modules are classified using spectral flow, the irreducible supercharacters are computed and a continuum version of the Verlinde formula is verified to give non-negative integer structure coefficients. Interpreting these coefficients as those of the Grothendieck ring of fusion, partial results on the true fusion ring and its indecomposable structures are deduced.

The task of classifying logarithmic conformal field theories, traditionally considered beyond reach, has become feasible by identifying an algebraic object that largely captures this classification. In some sense, the relevant algebraic tool is a braided analogue of the Howe/Schur--Weyl duality.

In the AdS/CFT correspondence, gauge theory calculations beyond the planar approximation correspond to quantum corrections in gravity or in string theory. Recently, the partition function on the three-sphere of Chern-Simons-matter theories has been computed at all orders in the 1/N expansion, and this leads to predictions for quantum corrections in M-theory/string theory. Using the ideas of effective field theory, we show that some of these corrections can be calculated reliably by doing one-loop calculations in supergravity. A similar reasoning has been used recently to calculate logarithmic corrections to black hole entropy, and we use it here to perform a successful test of AdS_4/CFT_3 beyond the leading, planar approximation.

Supersymmetry on curved spaces has recently attracted much attention, mainly as a tool towards the exact computation of quantum field theory observables via localization. Taking a holographic perspective, I will discuss how the conditions for rigid supersymmetry to be preserved on a curved boundary arise from the bulk supergravity Killing spinor equations. In particular, I will show that a four-dimensional superconformal field theory can be put on a curved, Lorentzian spacetime if and only if this admits a null conformal Killing vector. For a supersymmetric field theory with an R-symmetry, not necessarily conformal, the vector is further restricted to be Killing. After having presented some illustrative examples, I will conclude comparing with the Euclidean case.

Some issues of higher-spin (HS) gauge theory (in d+1>3) related to its cubic interactions and holography are discussed. After providing a very brief overview on the topic, I show how to construct all gauge consistent cubic interactions using the ambient-space formulation. Its number matches that of all possible 3pt functions, recently derived by other groups. However only one vertex corresponds to the free scalar CFT on the boundary, hence the metric-like version of the vertex encoded in Vasiliev's equation.

It will be shown that the dynamics of discrete (integer-valued) Hamiltonian cellular automata can only be consistently defined, if it is linear in the same sense that unitary evolution in quantum mechanics is linear. This suggests us to look for an invertible map between such automata and continuous quantum mechanical models. Based on sampling theory, such a map can indeed be constructed and leads to quantum mechanical models which incorporate a fundamental scale. The admissible observables, the one-to-one correspondence of the respective conservation laws, and the existence of solutions of the modified dispersion relation for stationary states are discussed. References: H.-T. Elze, Action principle for cellular automata and the linearity of quantum mechanics, Phys. Rev. A 89, 012111 (2014) [arXiv:1312.1615]; do., Journal of Physics: Conference Series 504 (2014) 012004 [arXiv:1403.2646].

The study of Superstring Theories on AdS backgrounds is important in the context of Gauge/Gravity correspondence. These theories can be reduced, under certain assumptions, to Sigma Models on semi-symmetric super-cosets. For a peculiar class of these cosets one can also introduce a WZW term. This correspond to study a Superstring Theory on a background supported by a mixture of RR and NSNS fluxes, as can happen for theories on $AdS_3\times S^3 \times M_4$. I will show the effect of this term on Integrability, Kappa symmetry and conformality of the theory, computing also the BMN spectrum in some relevant case for $AdS_3/CFT_2$ correspondence.

BPS states in N=2 gauge theories or string vacua are generically stable but liable to decay across certain codimension-one loci in moduli space. This process is easily understood by viewing BPS states as a bound state of more elementary BPS constituents, described classically by multi-centered solutions of the low energy effective action. The semi-classical quantization of the space of such solutions agrees with the wall-crossing formulae derived in the mathematical literature on BPS invariants, providing a physically elementary justification of the latter. Using this intuition, it is possible to express the BPS index, at any point in moduli space, in terms of indices associated to elementary (or single-centered) constituents. If time permits, I will present evidence for this idea in the case of BPS states described by quiver representations.

In the setting of integrability in AdS/CFT, in the typical approach to the AdS_5 x S^5 string a light-cone gauge is fixed, breaking Lorentz invariance on the worldsheet. One attempt to avoid the need for this goes under the name of Pohlmeyer reduction. Recently an S-matrix was conjectured to describe the scattering of solitons in this theory. Now as I will explain in my talk, the S-matrix of an integrable quantum field theory together with its dispersion relation are enough to find its finite volume spectrum exactly, through the so-called thermodynamic Bethe ansatz. I will work this out for an S-matrix and dispersion that interpolate between the standard light-cone gauge fixed superstring and this conjectured Pohlmeyer S-matrix, by analogy to a simpler model. Viewed as a deformation of the light-cone gauge fixed superstring TBA, this story is very similar to deforming the XXX spin chain to the XXZ one, which I will concretely discuss. I will finish by emphasizing important differences to this simple toy model, and discuss surprises in the so-called Y-system associated to the TBA equations.

Chiral anomalies have profound impact on the transport properties of relativistic fluids. They are closely related to the creation of currents by magnetic fields or vortices in the fluid via the so called Chiral Magnetic Conductivity and the Chiral Vortical Conductivity. Both can be computed by Kubo type formulae from special kinematic limits of two point functions of currents. I will review the calculation of these conductivites in a gas of free Weyl fermions and at strong coupling via a holographic model. A special and somewhat mysterious role is played by the mixed gauge-gravitational anomaly.