L3

In this talk we will discuss non-Abelian T-duality as a solution generating technique in type II Supergravity, briefly reviewing its potential to motivate, probe or challenge classifications of supersymmetric solutions, and focusing on the open problem of providing the newly generated AdS brackgrounds with consistent dual superconformal field theories. These can be seen as renormalization fixed points of linear quivers of increasing rank. As illustrative examples, we consider the non-Abelian T-duals of AdS5xS5, the Klebanov-Witten background, and the IIA reduction of AdS4xS7, whose proposed quivers are, respectively, the four dimensional N=2 Gaiotto-Maldacena theories describing the worldvolume dynamics of D4-NS5 brane intersections, its N=1 mass deformations realized as D4-NS5-NS5’, and the three dimensional N=4 Gaiotto-Witten theories, corresponding to D3-D5-NS5. Based on 1705.09661 and 1609.09061.

The horizon conjecture, proved in a case by case basis, states that every supersymmetric smooth horizon admits an sl(2, R) symmetry algebra. However it is unclear how string corrections modify the statement. In this talk I will present the analysis of supersymmetric near-horizon geometries in heterotic supergravity up to two loop order in sigma model perturbation theory, and show the conditions for the horizon to admit an sl(2, R) symmetry algebra. In the second part of the talk, I shall consider the inverse problem of determining all extreme black hole solutions associated to a prescribed near-horizon geometry. I will expand the horizon fields in the radial co-ordinate, the so-called moduli, and show that the moduli must satisfy a system of elliptic PDEs, which implies that the moduli space is finite dimensional.

The talk is based on arXiv:1605.05635 [hep-th] and arXiv:1610.09949 [hep-th].

I will start with briefly describing the HISH ( Holography Inspired Hadronic String) model and reviewing the fits of the spectra of mesons, baryons, glue-balls and exotic hadrons. 

I will present the determination of the hadron strong decay widths. The main decay mechanism is that of a string splitting into two strings. The corresponding total decay width behaves as $\Gamma =\frac{\pi}{2}A T L $ where T and L are the tension and length of the string and A is a dimensionless universal constant. The partial width of a given decay mode is given by $\Gamma_i/\Gamma = \Phi_i \exp(-2\pi C m_\text{sep}^2/T$ where $\Phi_i$ is a phase space factor, $m_\text{sep}$ is the mass of the "quark" and "antiquark" created at the splitting point, and C is adimensionless coefficient close to unity. I will show the fits of the theoretical results to experimental data for mesons and baryons. I will examine both the linearity in L and the exponential suppression factor. The linearity was found to agree with the data well for mesons but less for baryons. The extracted coefficient for mesons $A = 0.095\pm  0.01$  is indeed quite universal. The exponential suppression was applied to both strong and radiative decays. I will discuss the relation with string fragmentation and jet formation. I will extract the quark-diquark structure of baryons from their decays. A stringy mechanism for Zweig suppressed decays of quarkonia will be proposed and will be shown to reproduce the decay width of  states. The dependence of the width on spin and symmetry will be discussed. I will further apply this model to the decays of glueballs and exotic hadrons.

We study the spectrum of local operators living on a defect in a generic conformal field theory, and their coupling to the local bulk operators. We establish the existence of universal accumulation points in the spectrum at large s, s being the charge of the operators under rotations in the space transverse to the defect. Our main result is a formula that inverts the bulk to defect OPE, analogous to the Caron-Huot formula for the four-point function of CFTs without defects.

I am interested in the moduli spaces of heterotic vacua. These are closely related to the moduli spaces of stable holomorphic bundles but in which the base and bundle vary simultaneously, together with additional constraints deriving from string theory. I will first summarise some pre-Brexit results we have derived. These include an explicit Kaehler metric and Kaehler potential for both the moduli space and its first cousin, the matter field space. I will secondly describe new, post-Brexit work in which these results are encased within an elegant geometry, which we call a universal heterotic geometry. Beyond compelling aesthetics, the framework is surprisingly useful giving both a concise derivation of our pre-Brexit results as well as some new results. 

Let f be the planar Bargmann-Fock field, i.e. the analytic Gaussian field with covariance kernel exp(-|x-y|^2/2). We compute the critical point for the percolation model induced by the level sets of f. More precisely, we prove that there exists a.s. an unbounded component in {f>p} if and only if p<0. Such a percolation model has been studied recently by Beffara-Gayet and Beliaev-Muirhead. One important aspect of our work is a derivation of a (KKL-type) sharp threshold result for correlated Gaussian variables. The idea to use a KKL-type result to compute a critical point goes back to Bollobás-Riordan. This is joint work with Alejandro Rivera.

There are a huge number of nonlinear partial differential equations that do not have analytic solutions.   Often one can find similarity solutions, which reduce the number of independent variables, but still leads, generally, to a nonlinear equation.  This can, only sometimes, be solved analytically.  But always the solution is independent of the initial conditions.   What role do they play?   It is generally stated that the similarity  solution agrees with the (not determined) exact solution when (for some variable say t) obeys t >> t_1.   But what is  t_1?   How does it depend on the initial conditions?  How large must  t be for the similarity solution to be within 15, 10, 5, 1, 0.1, ….. percent of the real solution?   And how does this depend on the parameters and initial conditions of the problem?   I will explain how two such typical, but somewhat different, fundamental problems can be solved, both analytically and numerically,  and compare some of the results with small scale laboratory experiments, performed during the talk.  It will be suggested that many members of the audience could take away the ideas and apply them in their own special areas.

Numerical methods for SDEs typically use only the discretized increments of the driving Brownian motion. As one would expect, this approach is sensible and very well studied.

In addition to generating increments, it is also straightforward to generate time integrals of Brownian motion. These quantities give extra information about the Brownian path and are known to improve the strong convergence of methods for one-dimensional SDEs. Despite this, numerical methods that use time integrals alongside increments have received less attention in the literature.

In this talk, we will develop some underlying theory for these time integrals and introduce a new numerical approach to SDEs that does not require evaluating vector field derivatives. We shall also discuss the possible implications of this work for multi-dimensional SDEs.