Abstract
We propose brane web configurations for D-type and E-type \( \mathcal{N} \) =(1,0) little string theories based on a trivalent or quadrivalent gluing of 5-brane web diagrams. Tri-/quadri-valent gluing is a powerful way of computing 5d/6d partition functions for supersymmetric gauge theories based on the topological vertex. We generalize the gluing techniques to little string theories by introducing a new compact direction and compute their supersymmetric partition functions on Omega-deformed ℝ4×T 2. As concrete examples, we consider little string theories arising from Type IIB NS5-branes probing D4 or D5 singularity. Their effective gauge theory descriptions as the affine D4 or D5 quiver gauge theory can be realized with quadrivalent or trivalent gluing, respectively. Based on these gluings of 5-brane webs, we compute their refined partition functions and compare them with the known results. We extend the computation of the partition function to little string theory engineered from IIB NS5-branes probing E6 singularity based on a trivalent gluing. We also discuss the generalization to higher rank cases and the symmetries of the partition functions.
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Acknowledgments
We thank Joonho Kim, Hee-Cheol Kim, and Kimyeong Lee for useful discussions. We acknowledge the hospitality at APCTP, Fudan university, USTC, YMSC Tsinghua university where part of this work was done. SK is supported by the NSFC grant No. 12250610188 and also partially supported by the Fundamental Research Funds for the Central Universities 2682021ZTPY043. FY is supported by the NSFC grant No. 11950410490, by Start-up research grant YH1199911312101, and in part by Fundamental Research Funds for the Central Universities 2682021ZTPY043. The research of YS is supported by Samsung Science and Technology Foundation under Project Number SSTF-BA2002-05 and by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2018R1D1A1B07042934). XW is partially supported by NSFC grant No. 11950410490.
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Wei, XY., Sugimoto, Y., Yagi, F. et al. DE-type little strings from glued brane webs. J. High Energ. Phys. 2023, 214 (2023). https://doi.org/10.1007/JHEP05(2023)214
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DOI: https://doi.org/10.1007/JHEP05(2023)214