Physical systems with unexpected, or `hidden,’ symmetries have often played an important role in physics, beginning with the classical Kepler problem whose Laplace-Runge-Lenz vector ensures the closure of planetary orbits, and degeneracies of the Hydrogen spectrum. I will describe how precisely the same symmetry governs a unique four-dimensional quantum field theory, a maximally supersymmetric (`N=4') cousin of the strong-interaction Yang-Mills theory. After reviewing progress in recent years in using these symmetries to solve this model, I will describe novel applications involving massive particles. Combining the Laplace-Runge-Lenz vector with relativity then yields a novel way to calculate the spectrum of its Hydrogen-like bound states, including relativistic corrections. Based on 1408.0296.

One of the ways in which string theory differs from conventional field theories is that it has duality symmetries, which allow the construction of so-called non-geometric backgrounds, such as T-folds which have T-duality transition functions. String theory on a torus requires the introduction of dual coordinates conjugate to string winding number. This leads to physics and novel geometry in a doubled space, with non-trivial dynamics in the full doubled space-time. The geometry and physics of doubled space-time will be developed and discussed.

The BPS spectra of Class S theories are among the best understood, thanks in part to a construction known as Spectral Networks. We will review this framework and recent developments of it, and present results obtained through their applications.

Graduate Lectures: This short course will cover the origin of M-theory and brane physics with its applications.

Higher Gauge Theory is a categorical way of thinking about parallel transport of extended objects. Such parallel transport appears naturally within string and M-theory. In particular, the six-dimensional maximally superconformal theory or at least self-dual strings in four dimensions should be captured by Higher Gauge Theory. I will review some of my recent work in this area, including how M2-brane models fit into the picture, how twistor geometry can yield field equations containing the non-abelian tensor multiplet and give explicit higher versions of the BPST instanton and the 't Hooft-Polyakov monopole. If time permits, I will also talk a bit about a higher version of the IKKT matrix model.

In this talk I will explain how to compute gluon scattering amplitudes at finite coupling in planar N=4 SYM theory, using the duality with null polygonal Wilson loops, conformal symmetry, and the integrability of the colour flux tube dynamics. After introducing the main ideas and results, I will present some applications of this formalism at strong coupling and discuss the validity of the semiclassical (dual) string description.

I will discuss the gravitational dual of a mass deformation of N=4 SYM, called N=2* SYM, on S^4. Using holographic techniques one can calculate the universal contribution to the corresponding free energy in the planar limit and at large 't Hooft coupling. The result matches the expression recently computed using supersymmetric localization in the field theory. This agreement constitutes a non-trivial precision test of holography in a non-conformal setting. I will also briefly discuss the extension of these results to mass deformations of N=4 SYM with N=1 supersymmetry.

Graduate Lectures: This short course will cover the origin of M-theory and brane physics with its applications.

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 string dual. I will describe attempts to construct a large class of CFTs satisfying these conditions exploiting some technology of permutation orbifolds.

Graduate Lectures: This short course will cover the origin of M-theory and brane physics with its applications.

Graduate Lectures: This short course will cover the origin of M-theory and brane physics with its applications.

A central outcome of the recent Higgs discovery is that the Standard Model (SM) appears to be a selfconsistent quantum field theory all the way up to the Planck scale. Moreover, the measured values for the Higgs and top masses have an intriguing consequence for the question of stability of the Higgs vacuum: The SM lies close to the border of absolute electroweak vacuum stability and metastability. However, these celebrated results extrapolate the SM into a region where quantum gravity effects become important. We have therefore computed the quantum gravitational contributions to the standard model effective potential and analyzed their effects on the Higgs vacuum stability in the framework of effective field theory. Non-renormalizability of Einstein gravity induces higher dimension φ6 and φ8 operators at the one- loop level with novel couplings η1/2. We find that the true minimum of the standard model effective potential now lies below the Planck scale for almost the entire parameter space (η1/2(mt) > 0.01). In addition quantum gravity is shown to contribute to the minimal value of the standard model NLO effective potential at the percent level. The quantum gravity induced contributions yield a metastable vacuum for a large fraction of the parameter space in the flowing couplings η1/2.

Half BPS states (operators) in N=4 SYM are famously described by free fermions both at weak and strong coupling. I describe a set of conjectures for a preferred class of states in more general conformal field theories that can be tested in supergravity for when such a free fermion description might arise and some motivation for it applying generally. The states in question belong to the chiral ring of a supersymmetric conformal field theory that extremize an additional U(1) charge for fixed dimension and can be reduced to multi-traces of a composite matrix field, which is equivalent to using Young tableaux (Schur polynomials) as a basis. The main conjecture asserts that if the Young tableaux are orthogonal, then the set of extremal three point functions of traces to order 1/N are determined up to a single constant. The conjecture is extended further by providing an exact norm for the Schur basis and this norm arises from a set of free fermions for a generalized oscillator algebra.

In this talk, I will review basic features of the pure spinor superstring as well as recent progress to compute and compactly represent scattering amplitudes in this framework. A string-inspired organization scheme for amplitudes in both field- and string-theories will be described where the non-linearities of ten-dimensional super Yang-Mills theory are encoded in so-called multiparticle superfields. They allow to efficiently capture the polarization dependence through cubic diagrams where the intuitive mapping as well as the composition rules for amplitudes are guided by BRST invariance.

I will discuss recent developments in the duality between gauge fields and strings.

In this talk we will discuss the collective field theory approach towards understanding the holographic duality between Vasiliev's minimal higher spin theory in AdS4 and the free O(N) vector model in 2+1 dimensions.

I will review the link between 1+p dimensional maximally supersymmetric Yang-Mills and the black hole thermodynamics of Dp-branes via the gauge/string correspondence. The finite temperature behaviour of Dp-brane supergravity black holes looks very alien from the perspective of the dual strongly coupled Yang-Mills. However, I will argue that in a natural set of Yang-Mills variables, the classical moduli (which unfortunately are still strongly coupled), certain features of these thermodynamics become quite transparent.

I will discuss the exact quantum entropy of supersymmetric black holes as a gravitational functional integral in AdS2. In theories with eight supercharges, a computation of the exact entropy is possible using supersymmetric localization. I will discuss this technique, and describe the computation of functional determinants that can be computed using index theorems. I will then compare the exact gravitational formula to microscopic formulas coming from string theory.