Abstract
Recently, Kim, Shiu and Vafa proposed general consistency conditions for six dimensional supergravity theories with minimal supersymmetry coming from couplings to strings. We test them in explicit perturbative orientifold models in order to unravel the microscopic origin of these constraints. Based on the perturbative data, we conjecture the existence of null charges Q∙Q = 0 for any six-dimensional theory with at least one tensor multiplet, coupling to string defects of charge Q. We then include the new constraint to exclude some six-dimensional supersymmetric anomaly-free examples that have currently no string or F-theory realization. We also investigate the constraints from the couplings to string defects in case where supersymmetry is broken in tachyon free vacua, containing non-BPS configurations of brane supersymmetry breaking type, where the breaking is localized on antibranes. In this case, some conditions have naturally to be changed or relaxed whenever the string defects experience supersymmetry breaking, whereas the constraints are still valid if they are geometrically separated from the supersymmetry breaking source.
Highlights
To the Swampland [1,2,3], as opposed to the landscape of string theory compactifications
We investigate the constraints from the couplings to string defects in case where supersymmetry is broken in tachyon free vacua, containing nonBPS configurations of brane supersymmetry breaking type, where the breaking is localized on antibranes
2Interestingly enough, for our main 6d example, in was shown [37, 38] to be possible to have a supersymmetric model in F-theory [39] with the same supergravity spectrum, which is an isolated vacuum with no possible deformation parameters. It is not clear what type of constraints can be proposed, one finds that when supersymmetry is locally broken as in brane supersymmetry breaking (BSB) constructions, the constraints [7] are valid if the string defects are geometrically separated from the source of supersymmetry breaking
Summary
There are four types of supersymmetry multiplets appearing in 6d N = (1, 0) theories: gravity, vector, hyper and tensor multiplets. Their contributions to the anomaly polynomial is summarized in table 1. The polynomials X4α are parametrized in terms of (1 + NT )-dimensional vectors a, bi (with i labeling the gauge group factors). The group theory factors λi in table 2 are chosen such that one obtains integral scalar products a · a, a · bi, bi · bj ∈ Z (see [6]). When the spectrum is such that there is a six-dimensional anomaly, it can be cancelled by adding a tree-level Green-Schwarz term of the form. Induce a classical shift of (2.6) that cancels the anomalous shift of the action due to the spectrum
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