Abstract
We begin a study of the Higgs branch of six-dimensional (1, 0) little string theories governing the worldvolumes of heterotic ALE instantons. We give a description of this space by constructing the corresponding magnetic quiver. The latter is a three-dimensional \( \mathcal{N} \) = 4 quiver gauge theory that flows in the infrared to a fixed point whose quantum corrected Coulomb branches is the Higgs branch of the six-dimensional theory of interest. We present results for both types of heterotic strings, and mostly for ℂ2/ℤk ALE spaces. Our analysis is valid both in the absence and in the presence of small instantons. Along the way, we also describe small SO(32) instanton transitions in terms of the corresponding magnetic quiver, which parallels a similar treatment of the small E8 instanton transitions in the context of the E8 × E8 heterotic string.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Kapustin, On the universality class of little string theories, Phys. Rev. D 63 (2001) 086005 [hep-th/9912044] [INSPIRE].
N. Seiberg, New theories in six-dimensions and matrix description of M theory on T5 and T5/Z2, Phys. Lett. B 408 (1997) 98 [hep-th/9705221] [INSPIRE].
O. Aharony, A brief review of ‘little string theories’, Class. Quant. Grav. 17 (2000) 929 [hep-th/9911147] [INSPIRE].
A. Losev, G.W. Moore and S.L. Shatashvili, M & m’s, Nucl. Phys. B 522 (1998) 105 [hep-th/9707250] [INSPIRE].
C. Vafa, Evidence for F theory, Nucl. Phys. B 469 (1996) 403 [hep-th/9602022] [INSPIRE].
L. Bhardwaj, Classification of 6d \( \mathcal{N} \) = (1, 0) gauge theories, JHEP 11 (2015) 002 [arXiv:1502.06594] [INSPIRE].
L. Bhardwaj et al., F-theory and the Classification of Little Strings, Phys. Rev. D 93 (2016) 086002 [Erratum ibid. 100 (2019) 029901] [arXiv:1511.05565] [INSPIRE].
L. Bhardwaj, D.R. Morrison, Y. Tachikawa and A. Tomasiello, The frozen phase of F-theory, JHEP 08 (2018) 138 [arXiv:1805.09070] [INSPIRE].
L. Bhardwaj, Revisiting the classifications of 6d SCFTs and LSTs, JHEP 03 (2020) 171 [arXiv:1903.10503] [INSPIRE].
K.A. Intriligator, Compactified little string theories and compact moduli spaces of vacua, Phys. Rev. D 61 (2000) 106005 [hep-th/9909219] [INSPIRE].
K.A. Intriligator and N. Seiberg, Mirror symmetry in three-dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [INSPIRE].
J. de Boer et al., Mirror symmetry in three-dimensional theories, SL(2,Z) and D-brane moduli spaces, Nucl. Phys. B 493 (1997) 148 [hep-th/9612131] [INSPIRE].
J. de Boer, K. Hori, H. Ooguri and Y. Oz, Mirror symmetry in three-dimensional gauge theories, quivers and D-branes, Nucl. Phys. B 493 (1997) 101 [hep-th/9611063] [INSPIRE].
M. Porrati and A. Zaffaroni, M theory origin of mirror symmetry in three-dimensional gauge theories, Nucl. Phys. B 490 (1997) 107 [hep-th/9611201] [INSPIRE].
M. Del Zotto and K. Ohmori, 2-Group Symmetries of 6D Little String Theories and T-Duality, Annales Henri Poincare 22 (2021) 2451 [arXiv:2009.03489] [INSPIRE].
K.A. Intriligator, New string theories in six-dimensions via branes at orbifold singularities, Adv. Theor. Math. Phys. 1 (1998) 271 [hep-th/9708117] [INSPIRE].
P.S. Aspinwall and D.R. Morrison, Point-like instantons on K3 orbifolds, Nucl. Phys. B 503 (1997) 533 [hep-th/9705104] [INSPIRE].
P.S. Aspinwall, Point-like instantons and the Spin(32)/Z2 heterotic string, Nucl. Phys. B 496 (1997) 149 [hep-th/9612108] [INSPIRE].
K.A. Intriligator, RG fixed points in six-dimensions via branes at orbifold singularities, Nucl. Phys. B 496 (1997) 177 [hep-th/9702038] [INSPIRE].
J.D. Blum and K.A. Intriligator, Consistency conditions for branes at orbifold singularities, Nucl. Phys. B 506 (1997) 223 [hep-th/9705030] [INSPIRE].
J.D. Blum and K.A. Intriligator, New phases of string theory and 6-D RG fixed points via branes at orbifold singularities, Nucl. Phys. B 506 (1997) 199 [hep-th/9705044] [INSPIRE].
M. Gremm and A. Kapustin, Heterotic little string theories and holography, JHEP 11 (1999) 018 [hep-th/9907210] [INSPIRE].
A. Hanany and A. Zaffaroni, Branes and six-dimensional supersymmetric theories, Nucl. Phys. B 529 (1998) 180 [hep-th/9712145] [INSPIRE].
I. Brunner and A. Karch, Branes at orbifolds versus Hanany Witten in six-dimensions, JHEP 03 (1998) 003 [hep-th/9712143] [INSPIRE].
A. Hanany and A. Zaffaroni, Issues on orientifolds: On the brane construction of gauge theories with SO(2n) global symmetry, JHEP 07 (1999) 009 [hep-th/9903242] [INSPIRE].
M. Bullimore, T. Dimofte and D. Gaiotto, The Coulomb Branch of 3d \( \mathcal{N} \) = 4 Theories, Commun. Math. Phys. 354 (2017) 671 [arXiv:1503.04817] [INSPIRE].
A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230] [INSPIRE].
D. Gaiotto and E. Witten, S-Duality of Boundary Conditions In N = 4 Super Yang-Mills Theory, Adv. Theor. Math. Phys. 13 (2009) 721 [arXiv:0807.3720] [INSPIRE].
A. Sen, Dynamics of multiple Kaluza-Klein monopoles in M and string theory, Adv. Theor. Math. Phys. 1 (1998) 115 [hep-th/9707042] [INSPIRE].
E. Witten, Heterotic string conformal field theory and A-D-E singularities, JHEP 02 (2000) 025 [hep-th/9909229] [INSPIRE].
M. Del Zotto, M. Fazzi and S. Giri, A new vista on the Heterotic Moduli Space from Six and Three Dimensions, arXiv:2307.10356 [INSPIRE].
S. Cabrera, A. Hanany and M. Sperling, Magnetic quivers, Higgs branches, and 6d N =(1,0) theories, JHEP 06 (2019) 071 [Erratum ibid. 07 (2019) 137] [arXiv:1904.12293] [INSPIRE].
A. Dancer, F. Kirwan and A. Swann, Implosion for hyperkähler manifolds, arXiv:1209.1578 [INSPIRE].
A. Dancer, A. Hanany and F. Kirwan, Symplectic duality and implosions, Adv. Theor. Math. Phys. 25 (2021) 1367 [arXiv:2004.09620] [INSPIRE].
A. Kapustin and M.J. Strassler, On mirror symmetry in three-dimensional Abelian gauge theories, JHEP 04 (1999) 021 [hep-th/9902033] [INSPIRE].
E. Witten, SL(2, Z) action on three-dimensional conformal field theories with Abelian symmetry, in the proceedings of the From Fields to Strings: Circumnavigating Theoretical Physics: A Conference in Tribute to Ian Kogan, Oxford, U.K., January 8–10 (2004), p. 1173–1200 [hep-th/0307041] [INSPIRE].
A. Hanany and G. Zafrir, Discrete Gauging in Six Dimensions, JHEP 07 (2018) 168 [arXiv:1804.08857] [INSPIRE].
O. Bergman, M. Fazzi, D. Rodríguez-Gómez and A. Tomasiello, Charges and holography in 6d (1, 0) theories, JHEP 05 (2020) 138 [arXiv:2002.04036] [INSPIRE].
M. Fazzi and S. Giri, Hierarchy of RG flows in 6d (1, 0) orbi-instantons, JHEP 12 (2022) 076 [arXiv:2208.11703] [INSPIRE].
M. Fazzi, S. Giacomelli and S. Giri, Hierarchies of RG flows in 6d (1, 0) massive E-strings, JHEP 03 (2023) 089 [arXiv:2212.14027] [INSPIRE].
M. Fazzi, S. Giri and P. Levy, Proving the 6d a-theorem with the double affine Grassmannian, arXiv:2312.17178.
M. Del Zotto, M. Liu and P.-K. Oehlmann, Back to heterotic strings on ALE spaces. Part I. Instantons, 2-groups and T-duality, JHEP 01 (2023) 176 [arXiv:2209.10551] [INSPIRE].
M. Del Zotto, M. Liu and P.-K. Oehlmann, Back to Heterotic Strings on ALE Spaces: Part II — Geometry of T-dual Little Strings, arXiv:2212.05311 [INSPIRE].
M. Del Zotto, M. Liu and P.-K. Oehlmann, 6D Heterotic Little String Theories and F-theory Geometry: An Introduction, arXiv:2303.13502 [INSPIRE].
M. Del Zotto, M. Liu and P.-K. Oehlmann, Back to Heterotic Strings on ALE Spaces: Part III, in preparation.
M. Del Zotto, J.J. Heckman, A. Tomasiello and C. Vafa, 6d Conformal Matter, JHEP 02 (2015) 054 [arXiv:1407.6359] [INSPIRE].
J.J. Heckman and T. Rudelius, Top Down Approach to 6D SCFTs, J. Phys. A 52 (2019) 093001 [arXiv:1805.06467] [INSPIRE].
J.J. Heckman, T. Rudelius and A. Tomasiello, Fission, Fusion, and 6D RG Flows, JHEP 02 (2019) 167 [arXiv:1807.10274] [INSPIRE].
M. Del Zotto and G. Lockhart, Universal Features of BPS Strings in Six-dimensional SCFTs, JHEP 08 (2018) 173 [arXiv:1804.09694] [INSPIRE].
N.J. Hitchin, A. Karlhede, U. Lindstrom and M. Rocek, Hyperkahler Metrics and Supersymmetry, Commun. Math. Phys. 108 (1987) 535 [INSPIRE].
G.W. Moore and Y. Tachikawa, On 2d TQFTs whose values are holomorphic symplectic varieties, Proc. Symp. Pure Math. 85 (2012) 191 [arXiv:1106.5698] [INSPIRE].
E. Witten, Toroidal compactification without vector structure, JHEP 02 (1998) 006 [hep-th/9712028] [INSPIRE].
P.H. Ginsparg, Comment on Toroidal Compactification of Heterotic Superstrings, Phys. Rev. D 35 (1987) 648 [INSPIRE].
T. Mohaupt, Critical Wilson lines in toroidal compactifications of heterotic strings, Int. J. Mod. Phys. A 8 (1993) 3529 [hep-th/9209101] [INSPIRE].
P.S. Aspinwall and M.R. Plesser, Heterotic string corrections from the dual type II string, JHEP 04 (2000) 025 [hep-th/9910248] [INSPIRE].
E. Witten, Small instantons in string theory, Nucl. Phys. B 460 (1996) 541 [hep-th/9511030] [INSPIRE].
D.D. Frey and T. Rudelius, 6D SCFTs and the classification of homomorphisms ΓADE → E8, Adv. Theor. Math. Phys. 24 (2020) 709 [arXiv:1811.04921] [INSPIRE].
V.G. Kac, Infinite-Dimensional Lie Algebras, Cambridge University Press (1990) [https://doi.org/10.1142/9789812798343].
P. Hořava and E. Witten, Heterotic and type I string dynamics from eleven-dimensions, Nucl. Phys. B 460 (1996) 506 [hep-th/9510209] [INSPIRE].
P. Hořava and E. Witten, Eleven-dimensional supergravity on a manifold with boundary, Nucl. Phys. B 475 (1996) 94 [hep-th/9603142] [INSPIRE].
O.J. Ganor and A. Hanany, Small E8 instantons and tensionless noncritical strings, Nucl. Phys. B 474 (1996) 122 [hep-th/9602120] [INSPIRE].
S. Cremonesi, G. Ferlito, A. Hanany and N. Mekareeya, Instanton Operators and the Higgs Branch at Infinite Coupling, JHEP 04 (2017) 042 [arXiv:1505.06302] [INSPIRE].
N. Mekareeya, K. Ohmori, Y. Tachikawa and G. Zafrir, E8 instantons on type-A ALE spaces and supersymmetric field theories, JHEP 09 (2017) 144 [arXiv:1707.04370] [INSPIRE].
F. Benini, Y. Tachikawa and D. Xie, Mirrors of 3d Sicilian theories, JHEP 09 (2010) 063 [arXiv:1007.0992] [INSPIRE].
S. Cabrera and A. Hanany, Quiver Subtractions, JHEP 09 (2018) 008 [arXiv:1803.11205] [INSPIRE].
K. Gledhill and A. Hanany, Coulomb branch global symmetry and quiver addition, JHEP 12 (2021) 127 [arXiv:2109.07237] [INSPIRE].
A. Bourget et al., Branes, Quivers, and the Affine Grassmannian, Adv. Stud. Pure Math. 88 (2023) 331 [arXiv:2102.06190] [INSPIRE].
G. Ferlito, A. Hanany, N. Mekareeya and G. Zafrir, 3d Coulomb branch and 5d Higgs branch at infinite coupling, JHEP 07 (2018) 061 [arXiv:1712.06604] [INSPIRE].
S. Cabrera, A. Hanany and A. Zajac, Minimally Unbalanced Quivers, JHEP 02 (2019) 180 [arXiv:1810.01495] [INSPIRE].
D. Bashkirov and A. Kapustin, Supersymmetry enhancement by monopole operators, JHEP 05 (2011) 015 [arXiv:1007.4861] [INSPIRE].
D. Bashkirov, Examples of global symmetry enhancement by monopole operators, arXiv:1009.3477 [INSPIRE].
F. Apruzzi et al., General prescription for global U(1)’s in 6D SCFTs, Phys. Rev. D 101 (2020) 086023 [arXiv:2001.10549] [INSPIRE].
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
K. Ohmori, H. Shimizu, Y. Tachikawa and K. Yonekura, 6d \( \mathcal{N} \) = (1, 0) theories on T2 and class S theories: Part I, JHEP 07 (2015) 014 [arXiv:1503.06217] [INSPIRE].
K. Ohmori, H. Shimizu, Y. Tachikawa and K. Yonekura, 6d \( \mathcal{N} \) = (1, 0) theories on S1/T2 and class S theories: part II, JHEP 12 (2015) 131 [arXiv:1508.00915] [INSPIRE].
N. Mekareeya, K. Ohmori, H. Shimizu and A. Tomasiello, Small instanton transitions for M5 fractions, JHEP 10 (2017) 055 [arXiv:1707.05785] [INSPIRE].
O. Chacaltana and J. Distler, Tinkertoys for Gaiotto Duality, JHEP 11 (2010) 099 [arXiv:1008.5203] [INSPIRE].
O. Chacaltana, J. Distler and Y. Tachikawa, Nilpotent orbits and codimension-two defects of 6d N = (2, 0) theories, Int. J. Mod. Phys. A 28 (2013) 1340006 [arXiv:1203.2930] [INSPIRE].
M. Berkooz et al., Anomalies, dualities, and topology of D = 6 N = 1 superstring vacua, Nucl. Phys. B 475 (1996) 115 [hep-th/9605184] [INSPIRE].
N. Mekareeya, The moduli space of instantons on an ALE space from 3d \( \mathcal{N} \) = 4 field theories, JHEP 12 (2015) 174 [arXiv:1508.06813] [INSPIRE].
S. Cremonesi, G. Ferlito, A. Hanany and N. Mekareeya, Coulomb Branch and The Moduli Space of Instantons, JHEP 12 (2014) 103 [arXiv:1408.6835] [INSPIRE].
D. Gaiotto and S.S. Razamat, Exceptional Indices, JHEP 05 (2012) 145 [arXiv:1203.5517] [INSPIRE].
M. Del Zotto, M. Fazzi, C. Lawrie and L. Mansi, Exploring T-dualities in little string theories, in preparation.
J. Conway and N.J.A. Sloane, Sphere Packings, Lattices and Groups, Springer, New York, NY (2010) [https://doi.org/10.1007/978-1-4757-2016-7].
D.J. Gross, J.A. Harvey, E.J. Martinec and R. Rohm, The Heterotic String, Phys. Rev. Lett. 54 (1985) 502 [INSPIRE].
P. Boyle Smith, Y.-H. Lin, Y. Tachikawa and Y. Zheng, Classification of chiral fermionic CFTs of central charge ≤ 16, arXiv:2303.16917 [INSPIRE].
B.C. Rayhaun, Bosonic Rational Conformal Field Theories in Small Genera, Chiral Fermionization, and Symmetry/Subalgebra Duality, arXiv:2303.16921 [INSPIRE].
C. Dong and G. Mason, Holomorphic Vertex Operator Algebras of Small Central Charges, math/0203005.
S. Kachru, Elementary introduction to Moonshine, arXiv:1605.00697 [INSPIRE].
S. Kachru, N.M. Paquette and R. Volpato, 3D String Theory and Umbral Moonshine, J. Phys. A 50 (2017) 404003 [arXiv:1603.07330] [INSPIRE].
B. Fraiman, M. Graña and C.A. Núñez, A new twist on heterotic string compactifications, JHEP 09 (2018) 078 [arXiv:1805.11128] [INSPIRE].
A. Font et al., Exploring the landscape of heterotic strings on Td, JHEP 10 (2020) 194 [arXiv:2007.10358] [INSPIRE].
B. Fraiman and H.P. De Freitas, Symmetry enhancements in 7d heterotic strings, JHEP 10 (2021) 002 [arXiv:2106.08189] [INSPIRE].
B. Fraiman and H.P. de Freitas, Freezing of gauge symmetries in the heterotic string on T4, JHEP 04 (2022) 007 [arXiv:2111.09966] [INSPIRE].
B. Fraiman, M. Graña, H. Parra De Freitas and S. Sethi, Non-Supersymmetric Heterotic Strings on a Circle, arXiv:2307.13745 [INSPIRE].
F.A. Cachazo and C. Vafa, Type I’ and real algebraic geometry, hep-th/0001029 [INSPIRE].
P. Goddard and D. Olive, Algebras, Lattices and Strings, in the proceedings of the Vertex Operators in Mathematics and Physics, New York, NY, November 10–17, (1983), p. 51–96. [https://doi.org/10.1007/978-1-4613-9550-8_5].
B. Vinberg, On groups of unit elements of certain quadratic forms, Mathematics of the USSR-Sbornik 16 (1972) 17.
O. Chacaltana, J. Distler and Y. Tachikawa, Gaiotto duality for the twisted A2N−1 series, JHEP 05 (2015) 075 [arXiv:1212.3952] [INSPIRE].
A. Hanany and A. Zaffaroni, Monopoles in string theory, JHEP 12 (1999) 014 [hep-th/9911113] [INSPIRE].
A. Braverman and M. Finkelberg, Pursuing the Double Affine Grassmannian I: Transversal Slices via Instantons on Ak-Singularities, Duke Math. J. 152 (2010) 175 [arXiv:0711.2083] [INSPIRE].
M. Finkelberg, Doule affine Grassmannians and Coulomb branches of 3d N = 4 quiver gauge theories, in the proceedings of the International Congress of Mathematicians, Rio de Janeiro, Brazil, August 01–09 (2018), p. 1279–1298 [arXiv:1712.03039] [INSPIRE].
A. Malkin, V. Ostrik and M. Vybornov, The minimal degeneration singularities in the affine Grassmannians, arXiv:0305095 [https://doi.org/10.48550/ARXIV.MATH/0305095].
H. Nakajima, Towards a mathematical definition of Coulomb branches of 3-dimensional \( \mathcal{N} \) = 4 gauge theories, I, Adv. Theor. Math. Phys. 20 (2016) 595 [arXiv:1503.03676] [INSPIRE].
A. Braverman, M. Finkelberg and H. Nakajima, Towards a mathematical definition of Coulomb branches of 3-dimensional \( \mathcal{N} \) = 4 gauge theories, II, Adv. Theor. Math. Phys. 22 (2018) 1071 [arXiv:1601.03586] [INSPIRE].
A. Braverman, M. Finkelberg and H. Nakajima, Coulomb branches of 3d\( \mathcal{N} \) = 4 quiver gauge theories and slices in the affine Grassmannian, Adv. Theor. Math. Phys. 23 (2019) 75 [arXiv:1604.03625] [INSPIRE].
A. Beauville, Symplectic singularities, Invent. Math. 139 (2000) 541.
S. Gukov, P.-S. Hsin and D. Pei, Generalized global symmetries of T[M] theories. Part I, JHEP 04 (2021) 232 [arXiv:2010.15890] [INSPIRE].
F. Carta, S. Giacomelli, N. Mekareeya and A. Mininno, Comments on Non-invertible Symmetries in Argyres-Douglas Theories, JHEP 07 (2023) 135 [arXiv:2303.16216] [INSPIRE].
E. Witten, Some comments on string dynamics, in the proceedings of the STRINGS 95: Future Perspectives in String Theory, Los Angeles, U.S.A., March 13–18 (1995), p. 501–523 [hep-th/9507121] [INSPIRE].
M. Aganagic and N. Haouzi, ADE Little String Theory on a Riemann Surface (and Triality), arXiv:1506.04183 [INSPIRE].
N. Haouzi and C. Schmid, Little String Origin of Surface Defects, JHEP 05 (2017) 082 [arXiv:1608.07279] [INSPIRE].
N. Haouzi and C. Schmid, Little String Defects and Bala-Carter Theory, arXiv:1612.02008 [INSPIRE].
L.F. Alday, D. Gaiotto and Y. Tachikawa, Liouville Correlation Functions from Four-dimensional Gauge Theories, Lett. Math. Phys. 91 (2010) 167 [arXiv:0906.3219] [INSPIRE].
S. Cabrera, A. Hanany and M. Sperling, Magnetic quivers, Higgs branches, and 6d \( \mathcal{N} \) = (1, 0) theories — orthogonal and symplectic gauge groups, JHEP 02 (2020) 184 [arXiv:1912.02773] [INSPIRE].
M. Sperling and Z. Zhong, Balanced B and D-type orthosymplectic quivers — magnetic quivers for product theories, JHEP 04 (2022) 145 [arXiv:2111.00026] [INSPIRE].
S. Giacomelli, M. Moleti and R. Savelli, Probing 7-branes on orbifolds, JHEP 08 (2022) 163 [arXiv:2205.08578] [INSPIRE].
Acknowledgments
We would like to thank Sergio Benvenuti, Stefano Cremonesi, Simone Giacomelli, Paul Levy, Muyang Liu, Lorenzo Mansi, Noppadol Mekareeya, Paul-Konstantin Oehlmann and Yuji Tachikawa for interesting discussion and useful correspondence, and Craig Lawrie for interesting discussion and for informing us of an upcoming publication on related subjects. MF would like to thank the University of Milano-Bicocca, the Pollica Physics Center, the University of Lancaster for their kind hospitality and support during various stages of this work, and the “Symplectic Singularities and Supersymmetric QFT” conference held at UPJV in Amiens for providing a stimulating environment. SG thanks the University of Milano-Bicocca for hospitality during various stages of this work. MF and SG gratefully acknowledge support from the Simons Center for Geometry and Physics, Stony Brook University (2023 Simons Physics Summer Workshop) at which some of the research for this paper was performed. The work of MDZ and MF has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 851931). MDZ also acknowledges support from the Simons Foundation Grant #888984 (Simons Collaboration on Global Categorical Symmetries). The work of MF is also supported in part by the Knut and Alice Wallenberg Foundation under grant KAW 2021.0170, the Swedish Research Council grant VR 2018-04438, the Olle Engkvists Stiftelse grant No. 2180108. The work of SG was conducted with funding awarded by the Swedish Research Council grant VR 2022-06157.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2307.11087
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Del Zotto, M., Fazzi, M. & Giri, S. The Higgs branch of heterotic ALE instantons. J. High Energ. Phys. 2024, 167 (2024). https://doi.org/10.1007/JHEP01(2024)167
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2024)167