Abstract
Abstract We present maximal supergravity in two dimensions with gauge group SO(9). The construction is based on selecting the proper embedding of the gauge group into the infinite-dimensional symmetry group of the ungauged theory. The bosonic part of the Lagrangian is given by a (dilaton-)gravity coupled non-linear gauged σ-model with Wess-Zumino term. We give explicit expressions for the fermionic sector, the Yukawa couplings and the scalar potential which supports a half-supersymmetric domain wall solution. The theory is expected to describe the low-energy effective action upon reduction on the D0-brane near-horizon warped AdS 2 ×S 8 geometry, dual to the supersymmetric (BFSS) matrix quantum mechanics.
Highlights
Is the case of interest in this paper, the dual field theory is the supersymmetric matrix quantum mechanics [17] which itself has been proposed as a non-perturbative definition of M-theory [18]
These equations are classically integrable, which leads to the existence of a linear system [22, 23] and an infinite-dimensional global symmetry group E9(9) [24], the centrally extended affine E8(8), which extends the target space isometries and can be realized on-shell on the equations of motion
We present the detailed construction of the supergravity relevant for the D0-brane near-horizon geometry including its full fermionic sector and scalar potential
Summary
This group is E9(9), the centrally extended affine extension of the E8(8) target space isometries This symmetry gives rise to an infinite tower of scalar fields which are related by on-shell duality equations. Which are the lowest members of an infinite hierarchy of dual potentials that exhibit the integrable structure underlying the classical theory Another formulation of the two-dimensional maximal supergravity which will turn out to be relevant for the constructions of this paper is obtained by direct dimensional reduction of the eleven-dimensional theory [37]. These dual scalar fields which are defined on-shell, will play an important role in the construction of the gauged theory.
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