Topology change from (heterotic) Narain T-duality

Abstract

We consider Narain T-duality on a nontrivially fibered n-torus bundle in the presence of a topologically nontrivial NS H flux. The action of the duality group on the topology and H flux of the corresponding type II and heterotic string backgrounds is determined. The topology change is specialized to the case of supersymmetric T 2 -fibered torsional string backgrounds with nontrivial H flux. We prove that it preserves the global tadpole condition in the total space as well as on the base of the torus fibration. We find that some of these T-dualities exchange half of the field strength of an unbroken U(1) gauge symmetry with the anti-selfdual part of the curvature of a physical circle fibration. We verify that such T-dualities indeed exchange the supersymmetry condition for the circle bundle with that of the gauge bundle.

New supersymmetric index of heterotic compactifications with torsion

“…Comparing the holomorphic part of the partition function (61) to the contribution of a left-moving fermion coming from a charged Fermi multiplet of the base GLSM, one has in the former case an independent sum over the spin structures (k, l) on the worldsheet two-torus, while in the latter case the spin structure is chosen periodic along both one-cycles. 12 This simple observation clarifies some statements about topology-changing T-dualities, mixing the torus and gauge bundles, that were originally proposed by Evslin and Minasian in [51] in the effective theory context, and discussed by one of the authors in the torsion GLSM framework [21] (see also [52] for related comments). Such duality, that exchanges a line bundle over the base S and a circle bundle at the fermionic radius, is indeed a symmetry of the twining partition function Z fy built from (61) Including the independent sum over the spin structures (k, l) of the latter does not respect this symmetry.…”

“…O(2, 2; Z) T-duality transformations are mapped, under the correspondence between rational Narain lattices and rational CFTs summarized above, to isometries of the triple providing the rational CFT data, hence preserve (68). It provides an elegant explanation of the invariance of this expression, which gives also the contribution of the torus bundle to the integrated Bianchi identity, under the perturbative duality group [51]; as we have shown, this property is intimately related to the rational nature of the Narain lattice.…”

Heterotic fluxes and supersymmetry

“…The 8-dimensional perspective makes it apparent that there is a large redundancy in the nominal classification of solutions -this is simply a consequence of the O(2, 18) duality of the T 2 -compactification: there are O(2, 18) transformations that allow us to exchange the "physical" U(1)s associated to the Kaluza-Klein reduced metric and B-field with the "gauge" U(1)s. Such T-duality relations have been explored in [30,31]. This does not mean that every compactification with a non-trivial T 2 -fibration is on a T -duality orbit of a T 2 × K3 compactification.…”

T-duality in gauged linear sigma-models with torsion

“…One notices that the contribution from the torus fibration is of the same sign as the Fermi multiplets anomaly, which will fit neatly with the perturbative dualities studied in the next sections. As was explained in [24], the integrated Bianchi identity, which is a measure of the five-brane charge, is indeed a natural T-duality invariant for this class of solutions, as far as dualities along the fivebrane worldvolume coordinates, that include the two-torus, are concerned.…”

“…In this note, as a modest step in this direction, we investigate dualities between the gauged linear sigma-models with torsion corresponding to principal two-torus bundles over K3, equipped with some holomorphic gauge bundle V , and (0, 2) GLSMs for T 2 × K3 with an additional line bundle over the K3 surface. Perturbative dualities of this sort have been already investigated from a target-space perspective [24][25][26], using the heterotic generalization of Buscher rules (for a review see [27]). It allowed to relate these seemingly distinct class of string backgrounds, however only at lowest order in α ′ ; this is not really satisfactory in the present context as these solutions involve typically compactification at string scale.…”