New higher-derivative invariants in N = 2 supergravity and the Gauss-Bonnet term

Abstract

A new class of N = 2 locally supersymmetric higher-derivative invariants is constructed based on logarithms of conformal primary chiral superfields. They characteristically involve a coupling to R µν 2 − 1 3 R 2 , which equals the non-conformal part of the GaussBonnet term. Upon combining one such invariant with the known supersymmetric version of the square of the Weyl tensor one obtains the supersymmetric extension of the Gauss-Bonnet term. The construction is carried out in the context of both conformal superspace and the superconformal multiplet calculus. The new class of supersymmetric invariants resolves two open questions. The first concerns the proper identification of the 4D supersymmetric invariants that arise from dimensional reduction of the 5D mixed gauge-gravitational Chern-Simons term. The second is why the pure Gauss-Bonnet term without supersymmetric completion has reproduced the correct result in calculations of the BPS black hole entropy in certain models.

Non-renormalization for non-supersymmetric black holes

“…In D = 4 there are two known distinct four derivative invariants [17,18]. They complete the two terms written explicitly in (1.2) with particular matter terms and take the schematic form E 4 + SUSY matter , W 2 + SUSY matter , (1.3) in an off-shell formalism.…”

“…A common quantitative measure of the logarithmic corrections is the contribution of these classically marginal operators to the trace of the renormalized energy momentum tensor 16) where E 4 is the Gauss-Bonnet invariant (2.8), the square of the Weyl tensor is 17) and the dots denote other four derivative operators, including those formed from matter fields. The notation is adopted from the scale anomaly of conformal field theory in nondynamical background geometries but the physical interpretation is different here.…”

“…The only known chiral multiplets that fit these criteria are the W 2 multiplet (introduced in [40] and reviewed in detail in [31,32,41]) and the T(logΦ) multiplet (introduced in [17]). In the following, we will discuss the basic structures needed to establish the form of the supersymmetric invariant (5.3) for each of these multiplets.…”

“…kinetic chiral multiplet has Weyl weight w = 2 and is denoted T(logΦ) [17]. The field content of the T(logΦ) multiplet are discussed in appendix B.4.…”

“…As discussed in [17], the supersymmetrized invariant (5.3) derived from the chiral multiplet = T(logΦ) can be written as…”