Self-duality and self-similarity of little string orbifolds

2016/05/09 by Stefan Hohenegger, Amer Iqbal, Soo-Jong Rey
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Brane #Combinatorics #Cosmology and Gravitation Theories #Duality (order theory) #Geometry #Homogeneous space #Mathematical analysis #Mathematical physics #Mathematics #Moduli space #Nonlinear Waves and Solitons #Partition function (quantum field theory) #Physics #Pure mathematics #Quantum mechanics #Relationship between string theory and quantum field theory #Sigma #Singularity #String (physics) #String duality #hep-th #math.AG

paper · pdf · doi:10.1103/physrevd.94.046006

published as Phys. Rev. D 94, 046006 (2016) · 49 pages, 4 figures

arxiv created 2016/05/09 · openalex publication_date 2016/08/19 · arxiv updated 2016/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study a class of N=(1,0) little string theories obtained from orbifolds of M-brane configurations. These are realized in two different ways that are dual to each other: either as M parallel M5-branes probing a transverse A_N\ensuremath-1 singularity or N M5-branes probing an A_M\ensuremath-1 singularity. These backgrounds can further be dualized into toric, noncompact 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 analyze in detail the free energies \mathrm\ensuremathΣ_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, \mathrm\ensuremathΣ_N,M is identical to NM times \mathrm\ensuremathΣ_1,1. This entails that the Bogomol'nyi-Prasad-Sommerfield (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 \mathrm\ensuremathΣ_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.

Citations

• New theories in six dimensions and matrix description of M-theory on T5 and
• Some Comments On String Dynamics
• N = 2 instanton effective action in Ω-background and D3/D(−1)-brane system in R-R background
• Point-like instantons on K3 orbifolds
• M‐strings, elliptic genera and N = 4 string amplitudes
• New phases of string theory and 6d RG fixed points via branes at orbifold singularities
• Branes at orbifolds versus Hanany Witten in six dimensions
• Elliptic Genera of Symmetric Products and Second Quantized Strings
• Worldsheet realization of the refined topological string
• F-theory and the classification of little strings