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M-Strings

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Abstract

M2 branes suspended between adjacent parallel M5 branes lead to light strings, the ‘M-strings’. In this paper we compute the elliptic genus of M-strings, twisted by maximally allowed symmetries that preserve 2d (2, 0) supersymmetry. In a codimension one subspace of parameters this reduces to the elliptic genus of the (4, 4) supersymmetric A n-1 quiver theory in 2d. We contrast the elliptic genus of N M-strings with the (4, 4) sigma model on the N-fold symmetric product of \({{\mathbb{R}}^4}\). For N = 1 they are the same, but for N > 1 they are close, but not identical. Instead the elliptic genus of (4, 4) N M-strings is the same as the elliptic genus of (4, 0) sigma models on the N-fold symmetric product of \({{\mathbb{R}}^4}\), but where the right-moving fermions couple to a modification of the tangent bundle. This construction arises from a dual A n-1 quiver 6d gauge theory with U(1) gauge groups. Moreover, we compute the elliptic genus of domain walls which separate different numbers of M2 branes on the two sides of the wall.

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Authors and Affiliations

  1. Jefferson Physical Laboratory, Harvard University, Cambridge, MA, 02138, USA

    Babak Haghighat, Guglielmo Lockhart & Cumrun Vafa

  2. Department of Physics, LUMS School of Science and Engineering, U-Block, D.H.A, Lahore, Pakistan

    Amer Iqbal

  3. Department of Mathematics, LUMS School of Science and Engineering, U-Block, D.H.A, Lahore, Pakistan

    Amer Iqbal

  4. International School of Advanced Studies (SISSA), via Bonomea 265, 34136, Trieste, Italy

    Can Kozçaz

  5. INFN, Sezione di Trieste, Trieste, Italy

    Can Kozçaz

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  1. Babak Haghighat
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  2. Amer Iqbal
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  3. Can Kozçaz
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  4. Guglielmo Lockhart
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  5. Cumrun Vafa
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Correspondence to Babak Haghighat.

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Communicated by H. Ooguri

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Haghighat, B., Iqbal, A., Kozçaz, C. et al. M-Strings. Commun. Math. Phys. 334, 779–842 (2015). https://doi.org/10.1007/s00220-014-2139-1

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