## Advances in Theoretical and Mathematical Physics

- Adv. Theor. Math. Phys.
- Volume 7, Number 5 (2003), 787-806.

### Supersymmetric Solutions with Fluxes from Algebraic Killing Spinors

Chethan N. Gowdigere, Dennis Nemeschansky, and Nicholas P. Warner

#### Abstract

We give a general framework for constructing supersymmetric
solutions in the presence of non-trivial fluxes of tensor gauge fields.
This technique involves making a general Ansatz for the metric and then
defining the Killing spinors in terms of very simple projectors on the spinor
fields. These projectors and, through them, the spinors, are determined
*algebraically* in terms of the metric Ansatz. The Killing spinor equations
then fix the tensor gauge fields algebraically, and, with the Bianchi identities,
provide a system of equations for all the metric functions.
We illustrate this by constructing an infinite family of massive flows that
preserve eight supersymmetries in *M*-theory. This family constitutes all the
radially symmetric Coulomb branch flows of the softly broken, large *N* scalar-fermion
theory on *M*2-branes. We reduce the problem to the solution of a single,
non-linear partial differential equation in two variables. This
equation governs the flow of the fermion mass, and the function that
solves it then generates the entire *M*-theory solution algebraically in terms of
the function and its first derivatives.
While the governing equation is non-linear, it has a very simple perturbation theory
from which one can see how the Coulomb branch is encoded.

#### Article information

**Source**

Adv. Theor. Math. Phys., Volume 7, Number 5 (2003), 787-806.

**Dates**

First available in Project Euclid: 22 March 2005

**Permanent link to this document**

https://projecteuclid.org/euclid.atmp/1111510430

**Mathematical Reviews number (MathSciNet)**

MR2045301

**Zentralblatt MATH identifier**

1056.81057

#### Citation

Gowdigere, Chethan N.; Nemeschansky, Dennis; Warner, Nicholas P. Supersymmetric Solutions with Fluxes from Algebraic Killing Spinors. Adv. Theor. Math. Phys. 7 (2003), no. 5, 787--806. https://projecteuclid.org/euclid.atmp/1111510430