A 4D IIB flux vacuum and supersymmetry breaking. Part I. Fermionic spectrum
J. Mourad, Augusto Sagnotti
Abstract
A bstract We consider the type-IIB supergravity vacua that include an internal T 5 , depend on a single coordinate r and respect a four-dimensional Poincaré symmetry, with the aim of highlighting low-energy spectra with broken supersymmetry and a bounded string coupling. These vacua are characterized by the flux Φ of the self-dual five form in the internal torus, the length ℓ of the interval described by the coordinate r , a dilaton profile that is inevitably constant and a strictly positive dimensionless parameter h . As ℓ → ∞ while retaining finite values for Φ and $$ \mathrm{\ell}{h}^{-\frac{5}{4}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℓ</mml:mi> <mml:msup> <mml:mi>h</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mfrac> <mml:mn>5</mml:mn> <mml:mn>4</mml:mn> </mml:mfrac> </mml:mrow> </mml:msup> </mml:math> , half of the original ten-dimensional supersymmetry is recovered, while finite values of ℓ break it completely. In the large- ℓ limit one boundary disappears but the other is still present, and is felt as a BPS orientifold by a probe brane. In this paper we focus on the fermionic zero modes and show that, although supersymmetry is broken for finite values of ℓ , they are surprisingly those of four-dimensional N = 4 supergravity coupled to five vector multiplets. Still, the gravitini can acquire masses via radiative corrections, absorbing four of the massless spin- $$ \frac{1}{2} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> modes.