Abstract
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.
Highlights
To realise the group of a conformal defect holographically we have to consider asymptotically AdSd+1 space with the isometry group broken from SO(2, d) down to SO(2, d − 1)
We have developed a simple first-order formalism for constructing AdSdsliced domain walls in asymptotically AdSd+1 spacetimes
We have shown that the entire solution is specified with the help of a single function, from which the spacetime geometry, scalar potential and scalar profile are derived
Summary
We present the general first order formalism for domain walls with AdS slices. We begin by reviewing the construction of [32, 34, 35] where a complex ”superpotential” (or a triplet of real superpotentials) is introduced allowing for the first order equations for the fields. We demonstrate how one of the real functions appearing in the ”superpotential” can be obtained from another one in the closed analytic form This observation brings the formalism for curved domain walls in the shape similar to that for flat domain walls, where the solution is completely specified by the single superpotential. Where the prime indicates differentiation with respect to σ The solutions to these equations have to satisfy an additional constraint (resulting from the Hamiltonian constraint in the original theory (2.1)). Any two scalar functions ω(σ) and θ(σ) satisfying the constraint (2.12) define a domain wall solution (provided that the potential V (σ) constructed out of them has at least one critical point). As was shown in [34] the formulation with the triplet is equivalent to that with a single complex superpotential
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