TY - JOUR

T1 - Non-compact duality, super-Weyl invariance and effective actions

AU - Kuzenko, Sergei M.

PY - 2020/7/1

Y1 - 2020/7/1

N2 - In both N = 1 and N = 2 supersymmetry, it is known that Sp(2n, ℝ) is the maximal duality group of n vector multiplets coupled to chiral scalar multiplets τ(x, θ) that parametrise the Hermitian symmetric space Sp(2n, ℝ)/U(n). If the coupling to τ is introduced for n superconformal gauge multiplets in a supergravity background, the action is also invariant under super-Weyl transformations. Computing the path integral over the gauge prepotentials in curved superspace leads to an effective action Γ[τ,τ¯] with the following properties: (i) its logarithmically divergent part is invariant under super-Weyl and rigid Sp(2n, ℝ) transformations; (ii) the super-Weyl transformations are anomalous upon renormalisation. In this paper we describe the N = 1 and N = 2 locally supersymmetric “induced actions” which determine the logarithmically divergent parts of the corresponding effective actions. In the N = 1 case, superfield heat kernel techniques are used to compute the induced action of a single vector multiplet (n = 1) coupled to a chiral dilaton-axion multiplet. We also describe the general structure of N = 1 super-Weyl anomalies that contain weight-zero chiral scalar multiplets ΦI taking values in a Kähler manifold. Explicit anomaly calculations are carried out in the n = 1 case.

AB - In both N = 1 and N = 2 supersymmetry, it is known that Sp(2n, ℝ) is the maximal duality group of n vector multiplets coupled to chiral scalar multiplets τ(x, θ) that parametrise the Hermitian symmetric space Sp(2n, ℝ)/U(n). If the coupling to τ is introduced for n superconformal gauge multiplets in a supergravity background, the action is also invariant under super-Weyl transformations. Computing the path integral over the gauge prepotentials in curved superspace leads to an effective action Γ[τ,τ¯] with the following properties: (i) its logarithmically divergent part is invariant under super-Weyl and rigid Sp(2n, ℝ) transformations; (ii) the super-Weyl transformations are anomalous upon renormalisation. In this paper we describe the N = 1 and N = 2 locally supersymmetric “induced actions” which determine the logarithmically divergent parts of the corresponding effective actions. In the N = 1 case, superfield heat kernel techniques are used to compute the induced action of a single vector multiplet (n = 1) coupled to a chiral dilaton-axion multiplet. We also describe the general structure of N = 1 super-Weyl anomalies that contain weight-zero chiral scalar multiplets ΦI taking values in a Kähler manifold. Explicit anomaly calculations are carried out in the n = 1 case.

KW - Supergravity Models

KW - Superspaces

KW - Supersymmetric Effective Theories

KW - Supersymmetry and Duality

UR - http://www.scopus.com/inward/record.url?scp=85088840795&partnerID=8YFLogxK

U2 - 10.1007/JHEP07(2020)222

DO - 10.1007/JHEP07(2020)222

M3 - Article

AN - SCOPUS:85088840795

SN - 1126-6708

VL - 2020

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 7

M1 - 222

ER -