Graviton propagators in supergravity and noncommutative gauge theory

Abstract

We investigate the graviton propagator in the type IIB supergravity background which is dual to 4 dimensional noncommutative gauge theory. We assume that the boundary is located not at the infinity but at the noncommutative scale where the string frame metric exhibits the maximum. We argue that the Neumann boundary condition is the appropriate boundary condition to be adopted at the boundary. We find that the graviton propagator behaves just as that of the 4 dimensional massless graviton. On the other hand, the non-analytic behaviors of the other Kaluza-Klein modes are not significantly affected by the Neumann boundary condition.

Quantum gravity, field theory and signatures of noncommutative spacetime

“…The process described here is similar to the mechanism of UV/IR mixing that occurs on a D-brane in a background B-field, which is related to tachyonic instabilities arising from the exchange of closed string modes in the bulk [94,95]. It is complementary to the derivation of the newtonian force law [96] and supergravity graviton propagators [97] from four-dimensional maximally supersymmetric noncommutative Yang-Mills theory.…”

Green-Schwarz superstring from type IIB matrix model

“…The on-shell condition is relevant only to external modes. In fact, we calculate the four point amplitude from the type IIB matrix model where the stringy effect is relevant [13]. The winding number w along the angular direction can be reinterpreted as light-cone momenta p in a T-dual interpretation.…”

“…In this interpretation, we obtain type IIA superstring theory. Indeed, vertex operators in GS lightcone superstring for the type IIA supergravity multiplet are constructed [13] from original vertex operators for the type IIB matrix model [8,14,15]. Vertex operators in the matrix model are utilized to show the localization of gravity on the D-brane [16] like a Randall-Sundrum model [17].…”

“…Although there is no dimensionful parameter in the IIB matrix model, once we select a certain background then the characteristic dimensionful parameter, which is called the noncommutative parameter, emerges. It is proposed that the self-dual scale of this theory exists at a noncommutative scale [5][6][7]. Another important property of the type IIB matrix model is supersymmetries.…”

Superstring vertex operators in type IIB matrix model

“…In this comparison, the identification of noncommutative scale 1 θ with string scale α ′ has played an important role, which we have adopted in the process of deriving the action [5]. Originally, the scale in NC gauge theory is identified with string scale in the dual supergravity description [20,25,26]. Since we take the commutative limit in our formulation, the direct relation between UV finiteness of string scattering amplitude and the regularization of UV divergence which give rise to UV/IR mixing effect in noncommutative gauge theory is unclear.…”