Abstract
We write down the supermembrane actions for M-theory backgrounds dual to general N=2 four-dimensional superconformal field theories. The actions are given to all orders in fermions and are in a particular κ-gauge. When an extra U(1) isometry is present, our actions reduce to κ-gauge fixed Green–Schwarz actions for the corresponding Type IIA backgrounds.
Highlights
N = 2 supersymmetric Yang-Mills (SYM) theories have played an important role in understanding the non-perturbative behaviour of gauge theories in four-dimensions [1]
In this paper we find a κ-gauge in which the Gaiotto and Maldacena (GM) supergeometry simplifies considerably, allowing us to write down explicit expressions for the BST action
The Killing spinors η of a supersymmetric solution of 11-dimensional supergravity satisfy the Killing Spinor Equations (KSE), which follow from the vanishing of the supersymmetry variation of the gravitino 2
Summary
In this paper we write down the explicit form of the Bergshoeff-Sezgin-Townsend (BST) action [10] for supermembranes in the GM background in a particular κ-gauge. For a generic background, knowing the spacetime bosonic fields is not sufficient to write down the BST action; one needs to know the full supergeometry. In this paper we find a κ-gauge in which the GM supergeometry simplifies considerably, allowing us to write down explicit expressions for the BST action. This feature of the proposed κ-gauge simplifies considerably the torsion constraints and allows us to write down explicit expressions for the supervielbein and superconnection, which can be be inserted into the BST action. We present our conclusions and include appendices on our gamma-matrix and superalgebra conventions
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