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Abstract:

We study the sub-structure of the heterotic Kähler moduli space due to the presence of non-Abelian internal gauge fields from the perspective of the four-dimensional effective theory. Internal gauge fields can be supersymmetric in some regions of the Kähler moduli space but break supersymmetry in others. In the context of the four-dimensional theory, we investigate what happens when the Kähler moduli are changed from the supersymmetric to the non-supersymmetric region. Our results provide a low-energy description of supersymmetry breaking by internal gauge fields as well as a physical picture for the mathematical notion of bundle stability. Specifically, we find that at the transition between the two regions an additional anomalous U(1) symmetry appears under which some of the states in the low-energy theory acquire charges. We compute the associated D-term contribution to the four-dimensional potential which contains a Kähler-moduli dependent Fayet-Iliopoulos term and contributions from the charged states. We show that this D-term correctly reproduces the expected physics. Several mathematical conclusions concerning vector bundle stability are drawn from our arguments. We also discuss possible physical applications of our results to heterotic model building and moduli stabilisation. © 2009 SISSA.

Abstract:

We study the compactification of M-theory on Calabi-Yau five-folds and the resulting = 2 super-mechanics theories. By explicit reduction from 11 dimensions, including both bosonic and fermionic terms, we calculate the one-dimensional effective action and show that it can be derived from an = 2 super-space action. We find that the Kähler and complex structure moduli of the five-fold reside in 2a and 2b super-multiplets, respectively. Constrained 2a super-multiplets arise from zero-modes of the M-theory three-form and lead to cross-couplings between 2a and 2b multiplets. Fermionic zero modes which arise from the (1,3) sector of the 11-dimensional gravitino do not have bosonic super-partners and have to be described by purely fermionic super-multiplets in one dimension. We also study the inclusion of flux and discuss the consistency of the scalar potential with one-dimensional = 2 supersymmetry and how it can be described in terms of a superpotential. This superpotential can also be obtained from a Gukov-type formula which we present. Supersymmetric vacua, obtained by solving the F-term equations, always have vanishing vacuum energy due to the form of this scalar potential. We show that such supersymmetric solutions exist for particular examples. Two substantial appendices develop the topology and geometry of Calabi-Yau five-folds and the structure of one-dimensional = 2 supersymmetry and supergravity to the level of generality required for our purposes. © SISSA 2009.

Abstract:

We explicitly describe, in the language of four-dimensional N = 1 supersymmetric field theory, what happens when the moduli of a heterotic Calabi-Yau compactification change so as to make the internal non-Abelian gauge fields non-supersymmetric. At the edge of the region in Kähler moduli space where supersymmetry can be preserved, an additional anomalous U (1) gauge symmetry appears in the four-dimensional theory. The D-term contribution to the scalar potential associated to this U (1) attempts to force the system back into a supersymmetric configuration and provides a consistent low-energy description of gauge bundle stability. © 2009 Elsevier B.V. All rights reserved.