Self-duality and self-similarity of little string orbifolds

Abstract : We study a class of ${\cal N}=(1,0)$ little string theories obtained from orbifolds of M-brane configurations. These are realised in two different ways that are dual to each other: either as $M$ parallel M5-branes probing a transverse $A_{N-1}$ singularity or $N$ M5-branes probing an $A_{M-1}$ singularity. These backgrounds can further be dualised into toric, non-compact Calabi-Yau threefolds $X_{N,M}$ which have double elliptic fibrations and thus give a natural geometric description of T-duality of the little string theories. The little string partition functions are captured by the topological string partition function of $X_{N,M}$. We analyse in detail the free energies $\Sigma_{N,M}$ associated with the latter in a special region in the K\"ahler moduli space of $X_{N,M}$ and discover a remarkable property: in the Nekrasov-Shatashvili-limit, $\Sigma_{N,M}$ is identical to $NM$ times $\Sigma_{1,1}$. This entails that the BPS degeneracies for any $(N,M)$ can uniquely be reconstructed from the $(N,M)=(1,1)$ configuration, a property we refer to as self-similarity. Moreover, as $\Sigma_{1,1}$ is known to display a number of recursive structures, BPS degeneracies of little string configurations for arbitrary $(N,M)$ as well acquire additional symmetries. These symmetries suggest that in this special region the two little string theories described above are self-dual under T-duality.
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Contributor : Sylvie Flores <>
Submitted on : Wednesday, May 11, 2016 - 9:30:55 AM
Last modification on : Thursday, March 15, 2018 - 11:40:10 AM

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S. Hohenegger, A. Iqbal, Soo-Jong Rey. Self-duality and self-similarity of little string orbifolds. Physical Review D, American Physical Society, 2016, 94 (4), pp.046006 ⟨10.1103/PhysRevD.94.046006⟩. ⟨in2p3-01314254⟩



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