This colloquium reviews old and new no go theorems that severely constrain possible interactions of massless high spin particles. Massive particles can interact with gauge fields and gravity, but often they are plagued by pathologies such as superluminal propagation in nontrivial backgrounds. The last part of the talk uses the example of open string theory to show that such pathologies can be avoided by an appropriate choice of non-minimal interactions.

We revisit the relationship between the 6D (2, 0) M5 CFT compactified on a circle to 5D maximally supersymmetric YM Gauge Theory. We show that in the broken phase 5D SYM contains a spectrum of soliton states that can be identified with the complete KK modes of an M2 ending on the M5's. This provides evidence that the (2,0) theory on a circle is equivalent to 5D SYM with no additional UV degrees of freedom, suggesting that the latter is in fact a well-defined quantum theory and possibly finite.

Understanding the phases of string theory in the strong curvature and high temperature regime, which is inaccessible to the field theory approximation, may provide insights about the physics of the very early Universe. Cosmological solutions can be described at the perturbative string level, arising as quantum or thermal instabilities of an initially flat background. Two major obstacles that typically prevent a perturbative treatment of the backreaction are the Hagedorn/tachyonic divergences that occur in such strong curvature and/or high temperature regions and the initial gravitational singularity (Big Bang), that always appears in the field theory approach. In this talk, I will present recent progress in tackling these problems within the framework of perturbative string theory. In particular, I will consider a special toy model whose high degree of symmetry may help uncover the stringy mechanism that protects the cosmological evolution from Hagedorn or gravitational type singularities.

Abstract: There has recently been considerable discussion of holographic backgrounds with Schrodinger and Lifshitz symmetry, motivated by condensed matter applications. Since the bulk spacetimes are not asymptotically AdS, there are however many subtleties in setting up a holographic dictionary. In this talk we will argue that Schrodinger spacetimes (along with some realizations of Lifshitz) can be understood in terms of deformations of conformal field theories which break the relativistic scaling symmetry, but preserve an anisotropic/non-relativistic scale symmetry. We will highlight how this fact restricts which condensed matter systems can be well modeled holographically, and we will briefly discuss how the entropy of Schrodinger black holes (so-callsed null warped black holes) in three dimensions can be understood in this framework.

In the context of gauge-gravity duality, consistent truncations have proved to be powerful solution-generating tools, their latest application being to the holographic description of condensed matter systems. In the talk, I will discuss a rich class of consistent truncations of type IIB supergravity on squashed Sasaki-Einstein manifolds, leading to N=4 or N=2 gauged supergravity in five dimensions. As examples of the several possible applications, I will present an approach to domain wall gradient flows, as well as a new class of AdS5 backgrounds on the T(1,1) coset, with a comment on some related Lifshitz solutions.

Various aspects of the geometry and the thermodynamics of black holes in gauged supergravities are explored. In such theories, where the gauge coupling or the cosmological constant can be thought of as an integration constant arising from a higher-dimensional origin, it becomes appropriate to think of it as an additional thermodynamic variable associated with a pressure. The conjugate variable defines a volume for the black hole, although its geometric interpretation becomes quite subtle if the black hole is rotating. Further geometric properties of the black holes are also explored, including an intriguing universal structure for the product of the horizon areas, which is suggestive of a possible dual field theory explanation for the microscopic entropy. Isoperimetric and hoop inequalities are also discussed.

Using 3-algebras we obtain a nonabelian system of equations that furnish a representation of the (2,0)-supersymmetric tensor multiplet. The on-shell conditions are quite restrictive so that the system can be reduced to five-dimensional super-Yang-Mills theory along with six-dimensional abelian (2,0) tensor multiplets. Possible applications to D4-branes and M5-branes are discussed.