Integral invariants in N=4 SYM and the effective action for coincident D-branes

TL;DR

This paper develops a superspace formalism to construct supersymmetric invariants in N=4 SYM, deriving effective action terms for coincident D-branes and exploring their superconformal multiplet structures.

Contribution

It introduces a method to systematically construct supersymmetric invariants in superspace, applied to D=4, N=4 SYM, D=6, (2,0) tensor, D=3, N=8 scalar multiplets, and supergravity.

Findings

Constructed F^2, F^4, and (F^5 + ∂^2 F^4) terms in D-brane effective actions.

Derived abelian and non-abelian ∂^4 F^4 invariants and identified double-trace invariants.

Connected invariants to superconformal multiplets and extended the formalism to supergravity.

Abstract

The construction of supersymmetric invariant integrals is discussed in a superspace setting. The formalism is applied to D=4, N=4 SYM and used to construct the F^2, F^4 and (F^5 + \del^2 F^4) terms in the effective action of coincident D-branes. The results are in agreement with those obtained by other methods. A simple derivation of the abelian \del^4 F^4 invariant is given and generalised to the non-abelian case. We also find some double-trace invariants. The invariants are interpreted in terms of superconformal multiplets: the F^2 and F^4 terms are given by one-half BPS multiplets, the (F^5+\del^2F^4) arises as a full superspace integral of the Konishi multiplet K and the abelian \del^4 F^4 term comes from integrating the fourth power of the field strength superfield. Counterparts of the abelian invariants are exhibited for the D=6,(2,0) tensor multiplet and the D=3, N=8 scalar multiplet. The method is also applied to D=4, N=8 supergravity. All invariants in the linearised theory (with SU(8) symmetry) which arise from partial superspace integrals are constructed.