Recently, it was proposed that a $$ T\overline{T} $$
T
T
¯
deformed CFT is dual to a gravity theory in an asymptotically AdS spacetime at finite radial cutoff. Motivated by this proposal, we explore some aspects of Hyperscaling Violating geometries at finite cutoff and zero temperature. We study holographic entanglement entropy, mutual information (HMI) and entanglement wedge cross section (EWCS) for entangling regions in the shape of strips. It is observed that the HMI shows interesting features in comparison to the very small cutoff case: it is a decreasing function of the cutoff. It is finite when the distance between the two entangling regions goes to zero. The location of its phase transition also depends on the cutoff, and decreases by increasing the cutoff. On the other hand, the EWCS is a decreasing function of the cutoff. It does not show a discontinuous phase transition when the HMI undergoes a first-order phase transition. However, its concavity changes. Moreover, it is finite when the distance between the two strips goes to zero. Furthermore, it satisfies the bound EW ≥ $$ \frac{I}{2} $$
I
2
for all values of the cutoff.
Sinha and Vafa [1] had conjectured that the SO Chern-Simons gauge theory on S 3 must be dual to the closed A-model topological string on the orientifold of a resolved conifold. Though the Chern-Simons free energy could be rewritten in terms of the topological string amplitudes providing evidence for the conjecture, we needed a novel idea in the context of Wilson loop observables to extract cross-cap c = 0, 1, 2 topological amplitudes. Recent paper of Marino [2] based on the work of Morton and Ryder [3] has clearly shown that the composite representation placed on the knots and links plays a crucial role to rewrite the topological string cross-cap c = 0 amplitude. This enables extracting the unoriented cross-cap c = 2 topological amplitude. In this paper, we have explicitly worked out the composite invariants for some framed knots and links carrying composite representations in U (N ) Chern-Simons theory. We have verified generalised Rudolph's theorem, which relates composite invariants to the invariants in SO(N ) Chern-Simons theory, and also verified Marino's conjectures on the integrality properties of the topological string amplitudes. For some framed knots and links, we have tabulated the BPS integer invariants for cross-cap c = 0 and c = 2 giving the open-string topological amplitude on the orientifold of the resolved conifold.
We consider dyonic black hole in hyperscaling violating Lifshitz theories arised in a four dimensional Einstein-Maxwell-dilaton system along with axion fields. Considering the linearised equation of relevant fluctuations in metric and gauge fields, we analytically compute thermoelectric conductivity of the dual theory using Dirichlet boundary condition and find agreement with conductivities obtained in near horizon analysis. We also study temperature dependence of the conductivities. *
We study SU(2)[Formula: see text]×[Formula: see text]U(1) gauge theory with Chern–Simons term, coupled to scalar field in adjoint, in a probe approximation by ignoring back reaction on metric. Considering a simple ansatz for non-Abelian gauge field with helical structure, we find it admits s-wave and p-wave phases along with their coexistence. We study free energies for different phases along with those for p-wave phases for different values of pitch and frequency dependence of optical conductivities below critical temperature.
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