Abstract
We discuss the connection between Weyl2 supergravity and superstrings and further discuss holography between 4-dimensional, mathcal{N} = 4 superconformal Weyl2 supergravity and mathcal{N} = 8, higher spin-four theory on AdS5. The Weyl2 plus Einstein supergravity theory is a special kind of a bimetric gravity theory and consists of a massless graviton multiplet plus an additional massive spin-two supermultiplet. Here, we argue that the additional spin-two field and its superpartners originate from massive excitations in the open string sector; just like the mathcal{N} = 4 super Yang-Mills gauge fields, they are localized on the world volume of D3-branes. The ghost structure of the Weyl action should be considered as an artifact of the truncation of the infinitely many higher derivative terms underlying the massive spin 2 action. In field theory, mathcal{N} = 4 Weyl2 supergravity exhibits superconformal invariance in the limit of vanishing Planck mass. In string theory the additional spin-two fields become massless in the tensionless limit. Therefore low string scale scenarios with large extra dimensions provide (almost) superconformal field theories with almost massless open string spin-two fields. The full mathcal{N} = 4 scalar potential including the Yang-Mills matter multiplets is presented and the supersymmetric vacua of Einstein Supergravity are shown, as expected, to be vacua of massive Weyl supergravity. Other vacua are expected to exist which are not vacua of Einstein supergravity. Finally, we identify certain spin-four operators on the 4-dimensional boundary theory that could be the holographic duals of spin-four fields in the bulk.
Highlights
We argue that the additional spin-two field and its superpartners originate from massive excitations in the open string sector; just like the N = 4 super Yang-Mills gauge fields, they are localized on the world volume of D3-branes
As we will discuss the second spin-two mode wμν is not contained in standard closed string gravitational sector, but it corresponds to the first massive open string excitations, namely to the massive excitations of the open string Yang-Mills gauge fields
In this paper we have discussed a special version of N = 4 supersymmetric bimetric gravity coupled to N = 4 super Yang-Mills gauge theory
Summary
The most general formulation of Einstein plus curvature-square gravity is described by an action containing the standard Einstein term plus the following two terms being second order in the curvature tensor:. We see that there is a massive spin-2 state (the second term in (2.11)) with mass given by the pole at k2 = gW2 MP2 which has opposite residue to the usual massles graviton, and describes a ghost spin-2 state This shows that the theory contains as propagating degrees the standard, massless spin-two graviton gμν plus an additional massive spin-two field wμν. An alternative way to see this is to write down a particular bimetric gravity theory with two spin-two fields gμν and wμν with the following two-derivative action [30]: d4x√−g MP2 R(g) + 2MP Gμν (g)wμν − MW2 (wμν wμν − aw). As shown [31], this procedure is equivalent to adding to the W 2 action an infinite number of higher derivative terms, which resemble to additional parameters of the ghost-free bimetric gravity theory.
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