First order formalism for the holographic duals of defect CFTs

We develop a first order formalism for constructing gravitational duals of conformal defects in a bottom up approach. Similarly as for the flat domain walls a single function specifies the solution completely. Using this formalism we construct several novel families of analytic solutions dual to conformal interfaces and boundaries. As a sample application we study the boundary OPE and entanglement entropy for one of the found defects.Comment: 28 pages, 3 figure

Asymptotic symmetries and geometry on the boundary in the first order formalism

Proper understanding of the geometry on the boundary of a spacetime is a critical step on the way to extending holography to spaces with non-AdS asymptotics. In general the boundary cannot be described in terms of the Riemannian geometry and the first order formalism is more appropriate as we show. We analyze the asymptotic symmetries in the first order formalism for large classes of theories on AdS, Lifshitz or flat space. In all cases the asymptotic symmetry algebra is realized on the first order variables as a gauged symmetry algebra. First order formalism geometrizes and simplifies the analysis. We apply our framework to the issue of scale versus conformal invariance in AdS/CFT and obtain new perspective on the structure of asymptotic expansions for AdS and flat spaces

New modes from higher curvature corrections in holography

In gravitational theories involving higher curvature corrections the metric describes additional degrees of freedom beyond the graviton. Holographic duality maps these to operators in the dual CFT. We identify infinite families of theories for which these new modes cannot be truncated and the usual Fefferman-Graham expansion needs to be modified. New massive gravity in three dimensions and critical gravity in four dimensions are particular representatives of these families. We propose modified expansion, study the near-boundary behaviour of the metric and derive fall-off properties of the additional modes in theories involving higher derivative corrections.Comment: 24 page

Holographic Renormalization for Fermions in Real Time

We consider the real-time holography on Anti-de-Sitter (AdS) and more generally on Lifshitz spacetimes for spinorial fields. The equation of motion for fermions on general Lifshitz space is derived. Analytically solvable cases are identified. On AdS space we derived time-ordered, time-reversed, advanced and retarded propagators with the correct i \epsilon-insertions. Using the Keldysh-Schwinger contour we also calculated a propagator on thermal AdS. For massless fermions on the Lifshitz spacetime with z=2 we calculated the Euclidean 2-point function and explored the structure of divergences of the on-shell action for general values of z and mass m. The covariant counterterm action is derived.Comment: Master's thesis with minor edits, 77 page

Holographic two-point functions for Janus interfaces in the D1/D5D1/D5 CFT

This paper investigates scalar perturbations in the top-down supersymmetric Janus solutions dual to conformal interfaces in the $D1/D5$ CFT, finding analytic closed-form solutions. We obtain an explicit representation of the bulk-to-bulk propagator and extract the two-point correlation function of the dual operator with itself, whose form is not fixed by symmetry alone. We give an expression involving the sum of conformal blocks associated with the bulk-defect operator product expansion and briefly discuss finite-temperature extensions. To our knowledge, this is the first two-point function computation for a fully-backreacted, top-down holographic defect.Comment: 30 pages, PDFLaTe

Lifshitz as a deformation of Anti-de Sitter

We consider holography for Lifshitz spacetimes with dynamical exponent z=1+epsilon^2, where epsilon is small. We show that the holographically dual field theory is a specific deformation of the relativistic CFT, corresponding to the z=1 theory. Treating epsilon as a small expansion parameter we set up the holographic dictionary for Einstein-Proca models up to order epsilon^2 in three and four bulk dimensions. We explain how renormalization turns the relativistic conformal invariance into non-relativistic Lifshitz invariance with dynamical exponent z=1+epsilon^2. We compute the two-point function of the conserved spin two current for the dual two-dimensional field theory and verify that it is Lifshitz invariant. Using only QFT arguments, we show that a particular class of deformations of CFTs generically leads to Lifshitz scaling invariance and we construct examples of such deformations.Comment: 70 pages; v2: references added and minor improvement

Lifshitz from AdS at finite temperature and top down models

We construct analytically an asymptotically Lifshitz black brane with dynamical exponent z=1+epsilon^2 in an Einstein-Proca model, where epsilon is a small parameter. In previous work we showed that the holographic dual QFT is a deformation of a CFT by the time component of a vector operator and the parameter epsilon is the corresponding deformation parameter. In the black brane background this operator additionally acquires a vacuum expectation value. We explain how the QFT Ward identity associated with Lifshitz invariance leads to a conserved mass and compute analytically the thermodynamic quantities showing that they indeed take the form implied by Lifshitz invariance. In the second part of the paper we consider top down Lifshitz models with dynamical exponent close to one and show that they can be understood in terms of vector deformations of conformal field theories. However, in all known cases, both the conformal field theory and its Lifshitz deformations have modes that violate the Breitenlohner-Freedman bound.Comment: 35 page

The conformal supercurrents in diverse dimensions and conserved superconformal currents

Given a conserved and traceless energy-momentum tensor and a conformal Killing vector, one obtains a conserved current. We generalise this construction to superconformal theories in three, four, five and six dimensions with various amounts of supersymmetry by working in the appropriate superspaces.Comment: 23 page