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Register a new userNon-critical holography and four-dimensional CFTs with fundamentals
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We find non-critical string backgrounds in five and eight dimensions, holographically related to four-dimensional conformal field theories with N=0 and N=1 supersymmetries. In the five-dimensional case we find an AdS_5 background metric for a string model related to non-supersymmetric, conformal QCD with large number of colors and flavors and discuss the conjectured existence of a conformal window from the point of view of our solution. In the eight-dimensional string theory, we build a family of solutions of the form AdS_5 x tilde{S}^3 with tilde{S}^3 a squashed three-sphere. For a special value of the ratio N_f/N_c, the background can be interpreted as the supersymmetric near-horizon limit of a system of color and flavor branes on R^{1,3} times a known four-dimensional generalization of the cigar. The N=1 dual theory with fundamental matter should have an IR fixed point only for a fixed ratio N_f/N_c. General features of the string/gauge theory correspondence for theories with fundamental flavors are also addressed.
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We consider counterterms for odd dimensional holographic CFTs. These counterterms are derived by demanding cut-off independence of the CFT partition function on $S^d$ and $S^1 times S^{d-1}$. The same choice of counterterms leads to a cut-off independent Schwarzschild black hole entropy. When treated as independent actions, these counterterm actions resemble critical theories of gravity, i.e., higher curvature gravity theories where the additional massive spin-2 modes become massless. Equivalently, in the context of AdS/CFT, these are theories where at least one of the central charges associated with the trace anomaly vanishes. Connections between these theories and logarithmic CFTs are discussed. For a specific choice of parameters, the theories arising from counterterms are non-dynamical and resemble a DBI generalization of gravity. For even dimensional CFTs, analogous counterterms cancel log-independent cut-off dependence.
We compute spinning four point functions in the quasi-fermionic three dimensional conformal field theory with slightly broken higher spin symmetry at finite tHooft coupling. More concretely, we obtain a formula for $langle j_s j_{tilde{0}} j_{tilde{0}} j_{tilde{0}} rangle$, where $j_s$ is a higher spin current and $j_{tilde{0}}$ is the scalar single trace operator. Our procedure consists in writing a plausible ansatz in Mellin space and using crossing, pseudo-conservation and Regge boundedness to fix all undetermined coefficients. Our method can potentially be generalised to compute all spinning four point functions in these theories.
We formulate four-dimensional conformal gravity with (Anti-)de Sitter boundary conditions that are weaker than Starobinsky boundary conditions, allowing for an asymptotically subleading Rindler term concurrent with a recent model for gravity at large distances. We prove the consistency of the variational principle and derive the holographic response functions. One of them is the conformal gravity version of the Brown-York stress tensor, the other is a `partially massless response. The on-shell action and response functions are finite and do not require holographic renormalization. Finally, we discuss phenomenologically interesting examples, including the most general spherically symmetric solutions and rotating black hole solutions with partially massless hair.
Quantum theory can be formulated with certain non-Hermitian Hamiltonians. An anti-linear involution, denoted by PT, is a symmetry of such Hamiltonians. In the PT-symmetric regime the non-Hermitian Hamiltonian is related to a Hermitian one by a Hermitian similarity transformation. We extend the concept of non-Hermitian quantum theory to gauge-gravity duality. Non-Hermiticity is introduced via boundary conditions in asymptotically AdS spacetimes. At zero temperature the PT phase transition is identified as the point at which the solutions cease to be real. Surprisingly for solutions containing black holes real solutions can be found well outside the quasi-Hermitian regime. These backgrounds are however unstable to fluctuations which establishes the persistence of the holographic dual of the PT phase transition at finite temperature.
We present the full charge and energy diffusion constants for the Einstein-Maxwell dilaton (EMD) action for Lifshitz spacetime characterized by a dynamical critical exponent $z$. Therein we compute the fully renormalized static thermodynamic potential explicitly, which confirms the forms of all thermodynamic quantities including the Bekenstein-Hawking entropy and Smarr-like relationship. Our exact computation demonstrates a modification to the Lifshitz Ward identity for the EMD theory. For transport, we target our analysis at finite chemical potential and include axion fields to generate momentum dissipation. While our exact results corroborate anticipated bounds, we are able to demonstrate that the diffusivities are governed by the engineering dimension of the diffusion coefficient, $[D]=2-z$. Consequently, a $beta$-function defined as the derivative of the trace of the diffusion matrix with respect to the effective lattice spacing changes sign precisely at $z=2$. At $z=2$, the diffusion equation exhibits perfect scale invariance and the corresponding diffusion constant is the pure number $1/d_s$ for both the charge and energy sectors, where $d_s$ is the number of spatial dimensions. Further, we find that as $ztoinfty$, the charge diffusion constant vanishes, indicating charge localization. Deviation from universal decoupled transport obtains when either the chemical potential or momentum dissipation are large relative to temperature, an echo of strong thermoelectric interactions.
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