We investigate the aspects of surface defects in a new class of 4d N=1 superconformal quiver theories named class S_k. As the first step, we focus on the construction of the surface defects in IR under the situation where the UV theories of class S_k are higgsed by giving the vevs to some fields and try to specify them as 2d N=(0,2) vortex string theories by computing its elliptic genera encoded in the IR description of the superconformal indices of class S_k. This picture is consistent with type IIA brane construction of the vortex strings. Another way to argue the surface defects is to see their actions on the superconformal indices as difference operators, and we would like to discuss whether such difference operators form the algebras labelled by the representations of SU(N) flavor symmetries.

I first describe the remarkably simple algebraic structure underlying covariant string field theory. No knowledge of string field theory and only very basic concepts of string theory are required for this. I then use this structure to construct the superstring field theory action recursively and discuss its relation to the decomposition of (super) moduli spaces. I will focus mostly on open string theory but will comment on the generalisation to closed string.

Lecture 3: "Toward a Synthesis of Chiral Rings and Chiral Algebras." I will aim to discuss some recent work that seeks to relate the objects introduced in the first two lectures. Given enough time, we may also discuss generalizations of these ideas.

In this talk I plan to introduce the Four-Dimensional-Formulation (FDF) regularisation scheme proposed in arXiv:1404.4783 [hep-ph], which allows a four-dimensional representation of the d-dimensional particles propagating in the loop. Within FDF, I present the computation of one-loop QCD corrections of the processes gg>>gggg and gg>>Hggg (in the heavy top limit). On the other hand, I show the extension of Colour-Kinematics relations in d-dimensions and their application to compute efficiently one-loop amplitudes.

Lecture 2: "Chiral Algebras and Higher-Dimensional Theories." I will review briefly review the construction of chiral algebras and then focus on their relationship with a particular sub-sector of operators in higher-dimensional theories. I will again focus mostly on 4D N=2 theories.

Lecture 1: "Chiral Rings, Moduli Spaces, and Conformal Manifolds." In this lecture I will review basic aspects of chiral operators, with a special focus on 4D theories with 8 Poincare supercharges (i.e., N=2 SUSY). Using these operators, I will discuss basic aspects of moduli spaces and conformal manifolds.

One-point functions of certain non-protected scalar operators in the defect CFT dual to the D3-D5 probe brane system with k units of world volume flux can be expressed as overlaps between Bethe eigenstates of the Heisenberg spin chain and a matrix product state. We present a closed expression of determinant form for these one-point functions, valid for any value of k. The determinant formula factorizes into the k=2 result times a k-dependent prefactor. Making use of the transfer matrix of the Heisenberg spin chain we recursively relate the matrix product state for higher even and odd k to the matrix product state for k=2 and k=3 respectively. We furthermore find evidence that the matrix product states for k=2 and k=3 are related via a ratio of Baxter's Q-operators. The general k formula has an interesting thermodynamical limit involving a non-trivial scaling of k, which indicates that the match between string and field theory one-point functions found for chiral primaries might be tested for non-protected operators as well. We revisit the string computation for chiral primaries and discuss how it can be extended to non-protected operators.

Mathematical models of natural language can be organised into logical and statistical. The former are based on grammatical structures of phrases and sentences and the latter on distributions of words in corpora of text. In joint work with Clark (Cambridge) and Coecke (Oxford), we developed a unifying framework where the distributions of words are composed to form distributions for phrases and sentences. This expanded the application domains of the statistical models -- e.g. automatic reasoning about similarity -- from words to phrases and sentences. On the theoretical side, our model extends the word-based setting from vectors to tensors. Tensors are main players in the mathematical models of quantum mechanics. In this talk, I will review the theory and applications of our model in simple terms and through examples. I will briefly explain how `entanglement', a concept arising from tensors in quantum mechanics, manifests itself and is used as a resource in the linguistic applications. I will also explain how the reasoning toolkit used in this model is the same as that of Abramsky and Coecke in their categorical Quantum Mechanics model.

The collision of black holes is a classic problem in the strong-field regime of general relativity, with no known closed-form solution. When exact solutions are not known, or perturbative expansions about known solutions are inadequate to capture the non-linear dynamics, the numerical solution of the Einstein field equations is required. The main purpose of this talk is to describe, in detail, the necessary ingredients for achieving stable Cauchy evolution of black hole collisions in asymptotically anti-de Sitter (AdS) spacetimes. I will begin by motivating this program in terms of the heavy-ion physics it is intended to clarify. I will then give an overview of anti-de Sitter space, the mapping to its dual boundary conformal field theory, and the method we use to numerically solve the fully non-linear Einstein field equations with AdS boundary conditions. As a concrete example of these ideas, I will describe simulations of stable AdS black hole mergers in 5 dimensions.

Antibranes in backgrounds that have charge dissolved in fluxes are a key ingredient in constructing a landscape (Multiverse) of deSitter vacua in String Theory, and also of constructing microstate solutions corresponding to non-supersymmetric near-extremal black holes. There are several regimes of parameters in which one can study the physics of these antibranes, and I will show that in the regime of parameters where their gravitational backreaction is important, antibranes have a naked singularity that cannot be resolved either by brane polarization or by cloaking with a black hole horizon, and that signals a tachyonic instability. I will also present recent evidence that the theory on the wordvolume of anti-D3 branes is finite to all loops. I will conclude by discussing the implications of these results for the Multiverse paradigm and for the Fuzzball proposal.

We discuss the energy flux constraints for conserved and non-conserved operators in an arbitrary higher dimensional CFT. We then consider a deep inelastic scattering thought experiment and show how to derive these and other bounds on the OPE coefficients of various operators.

We investigate measures of chaos and entanglement scrambling in rational conformal field theories in 1+1 dimensions. First, we derive a formula for the late time value of the out-of-time-order correlators for these class of theories. Our universal result can be expressed as a particular combination of the modular S-matrix elements known as anyon monodromy scalar. Next, in the explicit setup of a SU(N)k WZW model, we compare the late time behaviour of the out-of-time correlators and the purity. Interestingly, in the large-c limit, the purity grows logarithmically but the out-of-time-order correlators remain constant. Therefore, we find that some systems may display entanglement scrambling in the absence of chaos.

In this talk we will discuss the bootstrap program applied to four-dimensional N=2 superconformal field theories, with focus on analytical results. After a brief review of the protected subsector captured by a two-dimensional chiral algebra, we will show how analytic bounds on anomaly coefficients are obtained and constrain the space of allowed SCFTs. Finally we will comment the implications for the numerical bootstrap program.

I will present several new 3d N=2 dualities with super-potentials involving monopole operators. Some of the theories that I will discuss describe systems of D3 branes ending on pq-webs. In these cases 3d mirror symmetry is a consequence of S-duality.

Collabor8 is a day-long meeting for early career researchers in mathematical and theoretical physics on Thursday 18th February 2016. The purpose of the meeting is to encourage collaboration between PhD students and postdocs from different institutions and research specialisms working in the UK. The meeting will feature short presentations from selected speakers about ongoing research problems, in contrast to traditional longer seminars on completed work. These will form the basis of group discussions, where participants may share their expertise and suggest new approaches. The conference website provides a convenient social network to promote continuing interaction after the meeting. We are delighted that Professor Luis Fernando Alday will be delivering a keynote lecture at the meeting. There is no conference fee, and funds are available to reimburse travel expenses. Further information about the meeting, including the registration form, may be found on the website below. The deadline for registration is Thursday 4th February. http://www.collabor8research.org

I will show that the matter content of the Standard Model takes a simple form when expressed in terms of world-lines of spinning particles and set this in the context of an effective string theory of the Standard Model described by tensionless spinning strings with contact interactions.

In the last fifteen years an extensive and successful program has been carried out, consisting in the application of integrability techniques to the study of the AdS/CFT correspondence in the planar limit. In this talk we focus on a particular string background corresponding, on the dual side, to the expectation value of a cusped Wilson line. Recently the study of this background has been boosted by the OPE program for polygonal Wilson loops and scattering amplitudes. In this talk we consider the quantum fluctuations of the worldsheet theory around the null cusp classical solution and we investigate various quantities of physical interest (free energy, dispersion relation, S-matrix) in the perturbative expansion at strong coupling. We also propose a possible discretization of this model which can be used to study the theory non-perturbatively through numerical lattice simulations.