On the supersymmetry and gauge structure of Matrix theory

Abstract

Supersymmetric Ward identity for the low energy effective action in the standard background gauge is derived for arbitrary trajectories of supergravitons in Matrix Theory. In our formalism, the quantum-corrected supersymmetry transformation laws of the supergravitons are directly identified in closed form, which exhibit an intricate interplay between supersymmetry and gauge (BRST) symmetry. As an application, we explicitly compute the transformation laws for the source-probe configuration at 1-loop and confirm that supersymmetry fixes the form of the action completely, including the normalization, to the lowest order in the derivative expansion. † kazama@hep3.c.u-tokyo.ac.jp ‡ tetsu@hep1.c.u-tokyo.ac.jp S gg = Tr dτ 1 2 −∂ τ A + i B m , X m 2 −iTr dτ C∂ τ [D τ , C] − gC B m , [X m , C] . (2.18) 6

Fully off-shell effective action and its supersymmetry in matrix theory: II

“…Finally, for terms containing 4 θ's or more, we apply appropriate SO(9) Fierz identities to reduce the expressions to truly independent ones. Let us describe this procedure for each ∆L (1) θ n more explicitly. In the following, A i ∼ E i will denote arbitrary constants.…”

“…Since, unlike for order 2, only a small portion of the fully off-shell 1-loop effective action Γ (1) was known at this order, we had to first complete its computation, including all the spin effects [2]. This was a horrendous task, involving manipulations of hundreds of terms in the intermediate stages.…”

“…We shall show this in the following way: Let us write the most general effective action up to 1-loop as Γ = Γ (0) + Γ (1) + ∆Γ (1) , where Γ (1) is our previous result and ∆Γ (1) is a possible arbitrary addition at order 4. Then, expanding δ ǫ also to 1-loop as δ ǫ = δ…”

High-Critical-Temperature Sm- and Nd-Based Superconductors Produced by Metal Organic Deposition Using Trifluoroacetates and Pentafluoropropionates

“…In a previous work [14], we gave a rather extensive discussion on the existing literature and emphasized the importance of the consistency of the approximation scheme in studying the symmetry of the effective action, which is an off-shell entity. We argued that the only consistent procedure is to deal with the trajectory, including the spin degrees of freedom, with an arbitrary time dependence and to adopt the derivative expansion according to the concept of order, defined as the number of derivatives plus half the number of fermions.…”

“…Only this scheme is free of the total derivative ambiguities inevitably present in the effective action. For further discussions, see section 3 of [14].…”