Quantum Fields and Strings

Two-dimensional non-linear sigma models on some supergroup manifolds are conformal field theories whether the action includes a Wess-Zumino term or not. These models are relevant for the worldsheet description of string theory in Anti-de Sitter backgrounds with Ramond-Ramond fluxes. The current algebra is an useful tool to study these theories. In these lectures I will review the construction of the current algebra. Then I will discuss some applications to the computation of the spectrum and integrability.

Two-dimensional non-linear sigma models on some supergroup manifolds are conformal field theories whether the action includes a Wess-Zumino term or not. These models are relevant for the worldsheet description of string theory in Anti-de Sitter backgrounds with Ramond-Ramond fluxes. The current algebra is an useful tool to study these theories. In these lectures I will review the construction of the current algebra. Then I will discuss some applications to the computation of the spectrum and integrability.

In this talk, I will show that the five-dimensional Maxwell theory with a Chern-Simons coupling larger than a critical value in the Reissner-Nordstrom black hole geometry has tachyonic modes. This instability has an interesting property that it happens only at non-vanishing momenta, suggesting a spatially modulated phase transition in the holographically dual field theory. The final state after the phase transition has taken place will be discussed in detail in a special limit

The seminar is devoted to the solution of the AdS/CFT spectral problem, both for infinite and finite volume cases, using integrability. The basic constructions will be explained using an analogy with the relativistic O(4) sigma model. We devote a special attention to the study of the so called dressing factor. This is a scalar factor of the scattering matrix fixed using discrete crossing symmetry. We will show how to explicitly solve the equations dictated by the crossing symmetry, discuss essential properties of the dressing factor and give a shorthand and suggestive notation for the Bethe Ansatz of AdS/CFT. Then we will sketch a shorthand way to pass from the Bethe Ansatz to the Y-system.

A systematic method to construct 4d N=2 supersymmetric theories by compactifying M5-branes on a Riemann surface was found by Gaiotto last year. This suggests that any physical quantity of the 4d theory should be reflected in another physical quantity of the 2d theory living on the Riemann surface. Indeed, one finds that the instanton partition function of the 4d theories equals the conformal blocks of the 2d theory. I would like to illustrate this construction through explicit examples.

We apply newly-developed techniques for studying perturbative scattering amplitudes to gauge theories with matter. It is well known that the N=4 SYM theory has a very simple S-matrix; do other gauge theories see similar simplifications in their S-matrices? It turns out the one-loop gluon S-matrix simplifies if the matter representations satisfy some group theoretic constraints. In particular, these constraints can be expressed as linear Diophantine equations involving the higher order Indices (or higher-order Casimirs) of these representations. We solve these constraints to find examples of theories whose gluon scattering amplitudes are as simple as those of the N=4 theory. This class includes the N=2, SU(K) theory with a symmetric and anti-symmetric tensor hypermultiplet. Non-supersymmetric theories with appropriately tuned matter content can also see remarkable simplifications. We find an infinite class of non-supersymmetric amplitudes that are cut-constructible even though naive power counting would suggest the presence of rational remainders.

Two of the most exciting observables in the cosmic microwave background (CMB) radiation, which could deeply impact our picture of the early universe, are non-Gaussianity and tensor modes. A potential detection of tensor modes can be explained in terms of a model of large field inflation. Theoretical considerations suggest that a symmetry should be invoked in order to protect the flatness of the inflaton potential and hence an axion enjoying a shift symmetry is a natural candidate. As main example, I will present a model of inflation in string theory based on axion monodromy. Non-perturbative effects typically correct the axion potential leading to small sinusoidal modulations on top of an otherwise flat slow roll potential. It can be shown analytically that a resonance between the oscillations of the background and the oscillations of the curvature fluctuations is responsible for the production of an observably large non-Gaussian signal. An explicit expression for the shape of this resonant non-Gaussianity will be presented. There is essentially no overlap between this shape and the local, equilateral, and orthogonal shapes, and in fact resonant non-Gaussianity is not captured by the simplest version of the effective field theory of inflation. Hopefully the analytic expression for resonant non-Gaussianity will be useful to further observationally constrain this class of models.

F-theory based vacua provide a potentially promising starting point for realizing Grand Unified Theories (GUTs) in string theory. In minimal realizations of this framework based on a point of E8 unification, this turns out to be quite constraining, and leads to specific expectations for the form of supersymmetry breaking. We discuss how the parameters of the F-theory GUT determine the sparticle spectrum, and possible signatures at the LHC.

We show that when a volume of quark matter rotates, there is an axial current flowing along the rotation axis. This effect has been overlooked in all previous treatments of relativistic fluids until calculations using gauge/gravity duality indicate it existence. The effect is a manifestation of triangle anomalies, and may exhibit itself in heavy ion collisions with nonzero impact parameter.

We describe a class of non-Fermi liquid systems, using the AdS/CFT correspondence. The Fermi surfaces are studied by computing the response functions of fermionic operators. The scaling behavior near the Fermi surfaces is determined by conformal dimensions in an emergent IR CFT. The low-energy excitations near the Fermi momenta are not Landau quasiparticles. When the operator is marginal in the IR CFT, the full spectral function is precisely of the `marginal Fermi liquid' form, introduced as a phenomenological model of the `strange metal' phase of high temperature superconductors.

In the context of AdS/CFT correspondence the AdS_3/CFT_2 instance of the duality stands apart from other well studied cases, like AdS_5/CFT_4 or AdS_4/CFT_3. One of the reasons is that the CFT side of this duality is not a theory of matrices but rather a two dimensional orbifold based on the group of permutations. In this talk we will discuss some aspects of this theory. In particular a diagrammatic language, akin to Feynman diagrams used for gauge theories, will be developed. Moreover, we will compute a large set of protected quantities in a certain symmetric product orbifold CFT, and show that these are elegantly given in terms of Hurwitz numbers.