Abstract
We shall develop a general technique to obtain the super heat kernel coefficients of an arbitrary second order operator in $N=1$ superspace. We focus on the space of conformal supergravity here but the method presented is equally applicable for other types of superspace. The first three coefficients which determine the one-loop divergence of the corresponding quantum theory will be calculated. As an application we shall present the one-loop logarithmic divergence of super Yang-Mills theory coupled to a string dilaton $S$. This is the first superfield calculation for SYM with a non-trivial gauge kinetic function, which generalize the previous result with a constant coupling strength. We also demonstrate that the method presented can be extended to the case of third order operators, with the restriction that its third order part is composed of only spinor derivatives.
Highlights
Supersymmetry has been a major area of study for decades
It was widely believed to be a promising candidate for the low-energy effective theory of grand unified Planckscale physics
In recent years there has been a considerable amount of research into the quantum aspects of both supergravity and various supersymmetric theories in a supergravity background
Summary
Supersymmetry has been a major area of study for decades. In particular, supergravity—the supersymmetric counterpart of Einstein gravity—has drawn considerable attention. A general understanding of the super heat kernel would be helpful for the one-loop analysis of various supersymmetric theories, and this work is an attempt to demonstrate that this is a viable route. In our previous work [7] we already used the heat-kernel method to consider super Yang-Mills (SYM) theory in conformal supergravity and analyzed its one-loop effective action. We consider a simple case in which the gauge kinetic function is diagonal in the gauge index and is determined by a single dilaton field S This typically arises from string theory models; for instance, it may come from a. It will be seen that the previously presented nonrecursive method is insufficient to calculate the heat-kernel coefficients of the above scenario after introducing a dilaton. We briefly argue that the method used here applies to a certain class of third-order operators, in which the third-order part contains only spinor derivatives
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
