Abstract
A rich pattern of gauge symmetries is found in the moduli space of heterotic string toroidal compactifications, at fixed points of the T-duality transformations. We analyze this pattern for generic tori, and scrutinize in full detail compactifications on a circle, where we find all the maximal gauge symmetry groups and the points where they arise. We present figures of two-dimensional slices of the 17-dimensional moduli space of Wilson lines and circle radii, showing the rich pattern of points and curves of symmetry enhancement. We then study the target space realization of the duality symmetry. Although the global continuous duality symmetries of dimensionally reduced heterotic supergravity are completely broken by the structure constants of the maximally enhanced gauge groups, the low energy effective action can be written in a manifestly duality covariant form using heterotic double field theory. As a byproduct, we show that a unique deformation of the generalized diffeomorphisms accounts for both SO(32) and E8 × E8 heterotic effective field theories, which can thus be considered two different backgrounds of the same double field theory even before compactification. Finally we discuss the spontaneous gauge symmetry breaking and Higgs mechanism that occurs when slightly perturbing the background fields, both from the string and the field theory perspectives.
Highlights
The distinct backgrounds of heterotic string theory on a k dimensional torus with constant metric, antisymmetric tensor field and Wilson lines are characterized by the points of theO(k,k+16;R) O(k;R)×O(k+16;R)×O(k,k+16;Z)coset manifold, where O(k, k + 16; Z) is theT-duality group [1, 2]
Comparing the string theory results with the spontaneous gauge symmetry breaking and Higgs mechanism in double field theory (DFT), we see that the masses acquired by the sligthly massive string states fully agree with those of the DFT fields, provided there is a specific relation between the vacuum expectation value of the scalars along the Cartan directions of the gauge group and the deviation of the metric, B-field and Wilson lines from the point of enhancement
In this paper we have analysed compactifications of the heterotic string on T k, focusing on the phenomenon of symmetry enhancement arising at special points and curves in moduli space
Summary
The distinct backgrounds of heterotic string theory on a k dimensional torus with constant metric, antisymmetric tensor field and Wilson lines are characterized by the points of the. The global duality symmetries are not manifest in heterotic supergravity To manifestly display these symmetries, as well as to account for the maximally enhanced gauge groups in a field theoretical setting, one appeals to the double field theory/generalized geometric reformulation of the string effective actions [9,10,11,12,13,14,15,16] (for reviews and more references see [17,18,19,20,21]). Comparing the string theory results with the spontaneous gauge symmetry breaking and Higgs mechanism in DFT, we see that the masses acquired by the sligthly massive string states fully agree with those of the DFT fields, provided there is a specific relation between the vacuum expectation value of the scalars along the Cartan directions of the gauge group and the deviation of the metric, B-field and Wilson lines from the point of enhancement. We count the number of non-vanishing structure constants of SO(32) and E8 × E8 in appendix G
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
