Abstract
Sigma models on semi-symmetric spaces provide the central building block for string theories on AdS backgrounds. Under certain conditions on the global supersymmetry group they can be made one-loop conformal by adding an appropriate fermionic Wess–Zumino term. We determine the full one-loop dilation operator of the theory. It involves an interesting new XXZ-like interaction term. Eigenvalues of our dilation operator, i.e. the one-loop anomalous dimensions, are computed for a few examples.
Highlights
Non-linear sigma models (NLSM), such as the famous O(N ) or CPN models, play an important role in high and low energy physics as well as mathematics
Research focused on cases in which the target is a symmetric space, i.e. can be written as a quotient G/H of agroup G by a subgroup H ⊂ G that is invariant under the action of an involution σ : G → G, i.e. by an automorphism of order two
There we describe the full one-loop dilation operator and we analyze the anomalous dimensions for a particular subset of fields
Summary
Non-linear sigma models (NLSM), such as the famous O(N ) or CPN models, play an important role in high and low energy physics as well as mathematics. The corresponding coset spaces G/H are often referred to as semi-symmetric and their sigma models appear as a part of the world-sheet action for strings in homogeneous AdS backgrounds, regardless of whether one works within the Green–Schwarz [1,2,3,4,5], pure spinor [6] or hybrid formalism [7,8]. In this paper we are not concerned with the relations between the different approaches [9,10,11,12,13,14] and pick the couplings in the action such that we recover the NLSM of the hybrid and pure spinor models In these cases, the metric conspires with a fermionic WZ term in order to make the action classically integrable and the one-loop beta-function vanish [15]. Auxiliary integral formulas, are collected in an appendix at the end of the paper
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