AdS Duals Research Articles

Qubit construction in 6D SCFTs

We consider a class of 6D superconformal field theories (SCFTs) which have a large N limit and a semi-classical gravity dual description. Using the quiver-like structure of 6D SCFTs we study a subsector of operators protected from large operator mixing. These operators are characterized by degrees of freedom in a one-dimensional spin chain, and the associated states are generically highly entangled. This provides a concrete realization of qubit-like states in a strongly coupled quantum field theory. Renormalization group flows triggered by deformations of 6D UV fixed points translate to specific deformations of these one-dimensional spin chains. We also present a conjectural spin chain Hamiltonian which tracks the evolution of these states as a function of renormalization group flow, and study qubit manipulation in this setting. Similar considerations hold for theories without AdS duals, such as 6D little string theories and 4D SCFTs obtained from compactification of the partial tensor branch theory on a T2.

DS/dS and Toverline{T}

The Toverline{T} deformation of a conformal field theory has a dual description as a cutoff AdS3 spacetime, at least at the level of pure 3d gravity. We generalize this deformation in such a way that it builds up a patch of bulk dS3 spacetime instead. At each step along the trajectory in the space of 2d theories, the theory is deformed by a specific combination of Toverline{T} and the two-dimensional cosmological constant. This provides a concrete holographic dual for the warped throat on the gravity side of the dS/dS duality, at leading order in large central charge. We also analyze a sequence of excitations of this throat on both sides of the duality, as well as the entanglement entropy. Our results point toward a mechanism for obtaining de Sitter solutions starting from seed conformal field theories with AdS duals.

On the classification of brane tilings

We present a computationally efficient algorithm that can be used to generate all possible brane tilings. Brane tilings represent the largest class of superconformal theories with known AdS duals in 3+1 and also 2+1 dimensions and have proved useful for describing the physics of both D3 branes and also M2 branes probing Calabi-Yau singularities. This algorithm has been implemented and is used to generate all possible brane tilings with at most 6 superpotential terms, including consistent and inconsistent brane tilings. The collection of inconsistent tilings found in this work form the most comprehensive study of such objects to date.

The exact superconformal R-symmetry minimizes [formula omitted

We present a new, general constraint which, in principle, determines the superconformal U ( 1 ) R symmetry of 4d N = 1 SCFTs, and also 3d N = 2 SCFTs. Among all possibilities, the superconformal U ( 1 ) R is that which minimizes the coefficient, τ R R , of its two-point function. Equivalently, the superconformal U ( 1 ) R is the unique one with vanishing two-point function with every non- R flavor symmetry. For 4d N = 1 SCFTs, τ R R minimization gives an alternative to a-maximization. τ R R minimization also applies in 3d, where no condition for determining the superconformal U ( 1 ) R had been previously known. Unfortunately, this constraint seems impractical to implement for interacting field theories. But it can be readily implemented in the AdS geometry for SCFTs with AdS duals.

Hidden Exceptional Global Symmetries in 4d CFTs

We study four dimensional N=1 gauge theories that arise on the worldvolume of D3-branes probing complex cones over del Pezzo surfaces. Global symmetries of the gauge theories are made explicit by using a correspondence between bifundamental fields in the quivers and divisors in the underlying geometry. These global symmetries are hidden, being unbroken when all inverse gauge couplings of the quiver theory vanish. In the broken phase, for finite gauge couplings, only the Cartan subalgebra is manifest as a global symmetry. Superpotentials for these models are constructed using global symmetry invariants as their building blocks. Higgsings connecting theories for different del Pezzos are immediately identified by performing the appropriate higgsing of the global symmetry groups. The symmetric properties of the quivers are also exploited to count the first few dibaryon operators in the gauge theories, matching their enumeration in the AdS duals.

Baryon Charges in 4d Superconformal Field Theories and Their AdS Duals

We consider general aspects of the realization of R and non-R flavor symmetries in the AdS_5 x H_5 dual of 4d N=1 superconformal field theories. We find a general prescription for computing the charges under these symmetries for baryonic operators, which uses only topological information (intersection numbers) on H_5. We find and discuss a new correspondence between the nodes of the SCFT quiver diagrams and certain divisors in the associated geometry. We also discuss connections between the non-R flavor symmetries and the enhanced gauge symmetries in non-conformal theories obtained by adding wrapped branes.

Cardy-Verlinde formula and entropy bounds in Kerr-Newman-AdS4/dS4black hole backgrounds

The Cardy-Verlinde formula is further verified by using the Kerr-Newman-AdS$_4$ and Kerr-Newman-dS$_4$ black holes. In the Kerr-Newman-AdS$_4$ spacetime, we find that, for strongly coupled CFTs with AdS duals, to cast the entropy of the CFT into the Cardy-Verlinde formula the Casimir energy must contains the terms $ -n ({\mathcal{J}} \Omega_H+ \frac{Q\Phi}{2}+ \frac{Q\Phi_0}{2})$, which associate with rotational and electric potential energies, and the extensive energy includes the term $-Q \Phi_0$. For the Kerr-Newman-dS$_4$ black hole, we note that the Casimir energy is negative but the extensive energy is positive on the cosmological horizon; while the Casimir energy is positive but the extensive energy is negative on the event horizon (the definitions for the two energies possess the same forms as the corresponding quantities of the Kerr-Newman-AdS$_4$ black hole). Thus we have to take the absolute value of the Casimir (extensive) energy in the Cardy-Verlinde formula for the cosmological (event) horizon. The result for the Kerr-Newman-dS$_4$ spacetime provides support of the dS/CFT correspondence. Furthermore, we also obtain the Bekenstein-Verlinde-like entropy bound for the Kerr-Newman-AdS$_4$ black hole and the D-bound on the entropy of matter system in Kerr-Newman-dS$_4$ spacetime. We find that both the bounds are tightened by the electric charge.

Cardy-Verlinde formula and AdS black holes

In a recent paper hep-th/0008140 by E. Verlinde, an interesting formula has been put forward, which relates the entropy of a conformal formal field in arbitrary dimensions to its total energy and Casimir energy. This formula has been shown to hold for the conformal field theories that have AdS duals in the cases of AdS Schwarzschild black holes and AdS Kerr black holes. In this paper we further check this formula with various black holes with AdS asymptotics. For the hyperbolic AdS black holes, the Cardy-Verlinde formula is found to hold if we choose the ``massless'' black hole as the ground state, but in this case, the Casimir energy is negative. For the AdS Reissner-Nordstr\"om black holes in arbitrary dimensions and charged black holes in D=5, D=4, and D=7 maximally supersymmetric gauged supergravities, the Cardy-Verlinde formula holds as well, but a proper internal energy which corresponds to the mass of supersymmetric backgrounds must be subtracted from the total energy. It is failed to rewrite the entropy of corresponding conformal field theories in terms of the Cardy-Verlinde formula for the AdS black holes in the Lovelock gravity.

CFT, holography, and causal entropy bound

The causal entropy bound (CEB) is confronted with recent explicit entropy calculations in weakly and strongly coupled conformal field theories (CFTs) in arbitrary dimension D. For CFTs with a large number of fields, N, the CEB is found to be valid for temperatures not exceeding a value of order M P /N 1 D−2 , in agreement with large N bounds in generic cut-off theories of gravity, and with the generalized second law. It is also shown that for a large class of models including high-temperature weakly coupled CFTs and strongly coupled CFTs with AdS duals, the CEB, despite the fact that it relates extensive quantities, is equivalent to (a generalization of) a purely holographic entropy bound proposed by E. Verlinde.