Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
139 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

The Higgs Branch of Heterotic LSTs: Hasse Diagrams and Generalized Symmetries (2312.05306v2)

Published 8 Dec 2023 in hep-th

Abstract: We study the Higgs branches of the 6d $(1,0)$ little string theories that live on the worldvolume of NS5-branes probing an ADE-singularity in the heterotic $E_8 \times E_8$ and $\mathrm{Spin}(32)/\mathbb{Z}_2$ string theories. On the $E_8 \times E_8$ side, such LSTs are obtained via fusion of orbi-instanton SCFTs. For the $\mathbb{C}2/\mathbb{Z}_K$ orbifolds, we determine a magnetic quiver for the Higgs branch from the alternative Type IIA brane system engineering the LST; we show that the magnetic quiver obtained in this way is the same as the Coulomb gauging of the 3d mirrors associated to the orbi-instanton building blocks. Using quiver subtraction, we determine the Hasse diagram of Higgs branch RG flows between the LSTs, and we analyze how the structure constants of the generalized global symmetries vary along the edges of the Hasse diagram. From the Hasse diagram of the Higgs branch, we are immediately able to identify LSTs with the same T-duality-invariant properties, and thus to propose candidate T-dual pairs. We perform a similar analysis of the Higgs branch Hasse diagram and putative T-dual families for particular $E_6$-orbifold LSTs by taking advantage of a duality between a rank zero orbi-instanton theory and a rank one conformal matter theory.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (104)
  1. O. Aharony, “A Brief Review of ‘Little String Theories’,” Class. Quant. Grav. 17 (2000) 929–938, arXiv:hep-th/9911147.
  2. H. Ahmed, P.-K. Oehlmann, and F. Ruehle, “T-Duality and Flavor Symmetries in Little String Theories,” arXiv:2311.02168 [hep-th].
  3. E. Alvarez, L. Alvarez-Gaume, and Y. Lozano, “An Introduction to T duality in string theory,” Nucl. Phys. B Proc. Suppl. 41 (1995) 1–20, arXiv:hep-th/9410237.
  4. F. Apruzzi, M. Fazzi, J. J. Heckman, T. Rudelius, and H. Y. Zhang, “General prescription for global U⁢(1)𝑈1U(1)italic_U ( 1 )’s in 6D SCFTs,” Phys. Rev. D 101 no. 8, (2020) 086023, arXiv:2001.10549 [hep-th].
  5. P. C. Argyres, J. J. Heckman, K. Intriligator, and M. Martone, “Snowmass White Paper on SCFTs,” arXiv:2202.07683 [hep-th].
  6. M. Artin, “Some numerical criteria for contractability of curves on algebraic surfaces,” Amer. J. Math. 84 (1962) 485–496. https://doi.org/10.2307/2372985.
  7. P. S. Aspinwall, “K3 surfaces and string duality,” in Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 96): Fields, Strings, and Duality, pp. 421–540. 11, 1996. arXiv:hep-th/9611137.
  8. P. S. Aspinwall and M. Gross, “Heterotic-heterotic string duality and multiple K3 fibrations,” Phys. Lett. B 382 (1996) 81–88, arXiv:hep-th/9602118.
  9. P. S. Aspinwall and M. Gross, “The SO(32) heterotic string on a K3 surface,” Phys. Lett. B 387 (1996) 735–742, arXiv:hep-th/9605131.
  10. P. S. Aspinwall and D. R. Morrison, “Point - like instantons on K3 orbifolds,” Nucl. Phys. B 503 (1997) 533–564, arXiv:hep-th/9705104.
  11. P. Bala and R. W. Carter, “Classes of unipotent elements in simple algebraic groups. I,” Math. Proc. Cambridge Philos. Soc. 79 no. 3, (1976) 401–425. https://doi.org/10.1017/S0305004100052403.
  12. P. Bala and R. W. Carter, “Classes of unipotent elements in simple algebraic groups. II,” Math. Proc. Cambridge Philos. Soc. 80 no. 1, (1976) 1–17. https://doi.org/10.1017/S0305004100052610.
  13. F. Baume, J. J. Heckman, and C. Lawrie, “6D SCFTs, 4D SCFTs, Conformal Matter, and Spin Chains,” Nucl. Phys. B 967 (2021) 115401, arXiv:2007.07262 [hep-th].
  14. F. Baume, J. J. Heckman, and C. Lawrie, “Super-spin chains for 6D SCFTs,” Nucl. Phys. B 992 (2023) 116250, arXiv:2208.02272 [hep-th].
  15. F. Baume, M. J. Kang, and C. Lawrie, “Two 6D origins of 4D SCFTs: Class S and 6D (1, 0) on a torus,” Phys. Rev. D 106 no. 8, (2022) 086003, arXiv:2106.11990 [hep-th].
  16. A. Beauville, “Symplectic singularities,” Inventiones Mathematicae 139 no. 3, (Mar, 2000) 541–549. https://doi.org/10.1007%2Fs002229900043.
  17. F. Benini, C. Córdova, and P.-S. Hsin, “On 2-Group Global Symmetries and their Anomalies,” JHEP 03 (2019) 118, arXiv:1803.09336 [hep-th].
  18. F. Benini, Y. Tachikawa, and D. Xie, “Mirrors of 3d Sicilian theories,” JHEP 09 (2010) 063, arXiv:1007.0992 [hep-th].
  19. 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 [hep-th].
  20. M. Berkooz, R. G. Leigh, J. Polchinski, J. H. Schwarz, N. Seiberg, and E. Witten, “Anomalies, dualities, and topology of D = 6 N=1 superstring vacua,” Nucl. Phys. B 475 (1996) 115–148, arXiv:hep-th/9605184.
  21. L. Bhardwaj, M. Del Zotto, J. J. Heckman, D. R. Morrison, T. Rudelius, and C. Vafa, “F-theory and the Classification of Little Strings,” Phys. Rev. D 93 no. 8, (2016) 086002, arXiv:1511.05565 [hep-th]. [Erratum: Phys.Rev.D 100, 029901 (2019)].
  22. M. Bianchi and A. Sagnotti, “On the systematics of open string theories,” Phys. Lett. B 247 (1990) 517–524.
  23. J. D. Blum and K. A. Intriligator, “Consistency conditions for branes at orbifold singularities,” Nucl. Phys. B 506 (1997) 223–235, arXiv:hep-th/9705030.
  24. 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) 199–222, arXiv:hep-th/9705044.
  25. A. Bourget, S. Cabrera, J. F. Grimminger, A. Hanany, M. Sperling, A. Zajac, and Z. Zhong, “The Higgs mechanism — Hasse diagrams for symplectic singularities,” JHEP 01 (2020) 157, arXiv:1908.04245 [hep-th].
  26. A. Bourget and J. F. Grimminger, “Fibrations and Hasse diagrams for 6d SCFTs,” JHEP 12 (2022) 159, arXiv:2209.15016 [hep-th].
  27. A. Bourget, J. F. Grimminger, A. Hanany, and Z. Zhong, “The Hasse diagram of the moduli space of instantons,” JHEP 08 (2022) 283, arXiv:2202.01218 [hep-th].
  28. A. Bourget, M. Sperling, and Z. Zhong, “Decay and Fission of Magnetic Quivers.” IN PREPARATION.
  29. A. Bourget, M. Sperling, and Z. Zhong, “Higgs Branch RG-flows via Decay and Fission.” IN PREPARATION.
  30. S. Cabrera and A. Hanany, “Branes and the Kraft-Procesi Transition,” JHEP 11 (2016) 175, arXiv:1609.07798 [hep-th].
  31. S. Cabrera and A. Hanany, “Quiver Subtractions,” JHEP 09 (2018) 008, arXiv:1803.11205 [hep-th].
  32. S. Cabrera, A. Hanany, and R. Kalveks, “Quiver Theories and Formulae for Slodowy Slices of Classical Algebras,” Nucl. Phys. B 939 (2019) 308–357, arXiv:1807.02521 [hep-th].
  33. S. Cabrera, A. Hanany, and M. Sperling, “Magnetic quivers, Higgs branches, and 6d N𝑁Nitalic_N=(1,0) theories,” JHEP 06 (2019) 071, arXiv:1904.12293 [hep-th]. [Erratum: JHEP 07, 137 (2019)].
  34. S. Cabrera, A. Hanany, and M. Sperling, “Magnetic quivers, Higgs branches, and 6d 𝒩𝒩\mathcal{N}caligraphic_N = (1, 0) theories — orthogonal and symplectic gauge groups,” JHEP 02 (2020) 184, arXiv:1912.02773 [hep-th].
  35. 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 [hep-th].
  36. C. Córdova, T. T. Dumitrescu, and K. Intriligator, “Exploring 2-Group Global Symmetries,” JHEP 02 (2019) 184, arXiv:1802.04790 [hep-th].
  37. C. Cordova, T. T. Dumitrescu, and K. Intriligator, “2-Group Global Symmetries and Anomalies in Six-Dimensional Quantum Field Theories,” JHEP 04 (2021) 252, arXiv:2009.00138 [hep-th].
  38. S. Cremonesi, G. Ferlito, A. Hanany, and N. Mekareeya, “Coulomb Branch and The Moduli Space of Instantons,” JHEP 12 (2014) 103, arXiv:1408.6835 [hep-th].
  39. S. Cremonesi, A. Hanany, N. Mekareeya, and A. Zaffaroni, “Tσρsuperscriptsubscriptabsent𝜌𝜎{}_{\rho}^{\sigma}start_FLOATSUBSCRIPT italic_ρ end_FLOATSUBSCRIPT start_POSTSUPERSCRIPT italic_σ end_POSTSUPERSCRIPT (G) theories and their Hilbert series,” JHEP 01 (2015) 150, arXiv:1410.1548 [hep-th].
  40. G. B. De Luca, A. Gnecchi, G. Lo Monaco, and A. Tomasiello, “Holographic duals of 6d RG flows,” JHEP 03 (2019) 035, arXiv:1810.10013 [hep-th].
  41. M. Del Zotto, M. Fazzi, and S. Giri, “A new vista on the Heterotic Moduli Space from Six and Three Dimensions,” arXiv:2307.10356 [hep-th].
  42. M. Del Zotto, M. Fazzi, and S. Giri, “The Higgs branch of heterotic ALE instantons,” arXiv:2307.11087 [hep-th].
  43. M. Del Zotto, J. J. Heckman, A. Tomasiello, and C. Vafa, “6d Conformal Matter,” JHEP 02 (2015) 054, arXiv:1407.6359 [hep-th].
  44. 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 [hep-th].
  45. M. Del Zotto, M. Liu, and P.-K. Oehlmann, “6D Heterotic Little String Theories and F-theory Geometry: An Introduction,” arXiv:2303.13502 [hep-th].
  46. 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 [hep-th].
  47. M. Del Zotto and K. Ohmori, “2-Group Symmetries of 6D Little String Theories and T-Duality,” Annales Henri Poincare 22 no. 7, (2021) 2451–2474, arXiv:2009.03489 [hep-th].
  48. F. Denef, “Les Houches Lectures on Constructing String Vacua,” Les Houches 87 (2008) 483–610, arXiv:0803.1194 [hep-th].
  49. C. D.H and M. W.M., Nilpotent Orbits in Semisimple Lie Algebras: An Introduction (1st ed.). Chapman and Hall/CRC, 1993. https://doi.org/10.1201/9780203745809.
  50. J. Distler, G. Elliot, M. J. Kang, and C. Lawrie, “Isomorphisms of 4D N=2 SCFTs from 6D,” Phys. Rev. D 107 no. 10, (2023) 106005, arXiv:2212.11983 [hep-th].
  51. J. Distler, M. J. Kang, and C. Lawrie, “Distinguishing 6D (1, 0) SCFTs: An extension to the geometric construction,” Phys. Rev. D 106 no. 6, (2022) 066011, arXiv:2203.08829 [hep-th].
  52. H. Elvang, D. Z. Freedman, L.-Y. Hung, M. Kiermaier, R. C. Myers, and S. Theisen, “On renormalization group flows and the a-theorem in 6d,” JHEP 10 (2012) 011, arXiv:1205.3994 [hep-th].
  53. 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 [hep-th].
  54. D. D. Frey and T. Rudelius, “6D SCFTs and the classification of homomorphisms ΓA⁢D⁢E→E8→subscriptΓ𝐴𝐷𝐸subscript𝐸8\Gamma_{ADE}\to E_{8}roman_Γ start_POSTSUBSCRIPT italic_A italic_D italic_E end_POSTSUBSCRIPT → italic_E start_POSTSUBSCRIPT 8 end_POSTSUBSCRIPT,” Adv. Theor. Math. Phys. 24 no. 3, (2020) 709–756, arXiv:1811.04921 [hep-th].
  55. D. Gaiotto, “N=2 dualities,” JHEP 08 (2012) 034, arXiv:0904.2715 [hep-th].
  56. D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, “Generalized Global Symmetries,” JHEP 02 (2015) 172, arXiv:1412.5148 [hep-th].
  57. D. Gaiotto, G. W. Moore, and A. Neitzke, “Wall-crossing, Hitchin systems, and the WKB approximation,” Adv. Math. 234 (2013) 239–403, arXiv:0907.3987 [hep-th].
  58. D. Gaiotto and E. Witten, “S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory,” Adv. Theor. Math. Phys. 13 no. 3, (2009) 721–896, arXiv:0807.3720 [hep-th].
  59. O. J. Ganor and A. Hanany, “Small E(8) instantons and tensionless noncritical strings,” Nucl. Phys. B 474 (1996) 122–140, arXiv:hep-th/9602120.
  60. P. H. Ginsparg, “Comment on Toroidal Compactification of Heterotic Superstrings,” Phys. Rev. D 35 (1987) 648.
  61. A. Giveon and M. Rocek, “Generalized duality in curved string backgrounds,” Nucl. Phys. B 380 (1992) 128–146, arXiv:hep-th/9112070.
  62. K. Gledhill and A. Hanany, “Coulomb branch global symmetry and quiver addition,” JHEP 12 (2021) 127, arXiv:2109.07237 [hep-th].
  63. H. Grauert, “Über Modifikationen und exzeptionelle analytische Mengen,” Math. Ann. 146 (1962) 331–368. https://doi.org/10.1007/BF01441136.
  64. A. Hanany and N. Mekareeya, “The small E88{}_{8}start_FLOATSUBSCRIPT 8 end_FLOATSUBSCRIPT instanton and the Kraft Procesi transition,” JHEP 07 (2018) 098, arXiv:1801.01129 [hep-th].
  65. A. Hanany and G. Zafrir, “Discrete Gauging in Six Dimensions,” JHEP 07 (2018) 168, arXiv:1804.08857 [hep-th].
  66. F. Hassler, J. J. Heckman, T. B. Rochais, T. Rudelius, and H. Y. Zhang, “T-Branes, String Junctions, and 6D SCFTs,” Phys. Rev. D 101 no. 8, (2020) 086018, arXiv:1907.11230 [hep-th].
  67. J. J. Heckman, S. Kundu, and H. Y. Zhang, “Effective field theory of 6D SUSY RG Flows,” Phys. Rev. D 104 no. 8, (2021) 085017, arXiv:2103.13395 [hep-th].
  68. J. J. Heckman, D. R. Morrison, T. Rudelius, and C. Vafa, “Atomic Classification of 6D SCFTs,” Fortsch. Phys. 63 (2015) 468–530, arXiv:1502.05405 [hep-th].
  69. J. J. Heckman, D. R. Morrison, T. Rudelius, and C. Vafa, “Geometry of 6D RG Flows,” JHEP 09 (2015) 052, arXiv:1505.00009 [hep-th].
  70. J. J. Heckman, D. R. Morrison, and C. Vafa, “On the Classification of 6D SCFTs and Generalized ADE Orbifolds,” JHEP 05 (2014) 028, arXiv:1312.5746 [hep-th]. [Erratum: JHEP 06, 017 (2015)].
  71. J. J. Heckman and T. Rudelius, “Top Down Approach to 6D SCFTs,” J. Phys. A 52 no. 9, (2019) 093001, arXiv:1805.06467 [hep-th].
  72. J. J. Heckman, T. Rudelius, and A. Tomasiello, “6D RG Flows and Nilpotent Hierarchies,” JHEP 07 (2016) 082, arXiv:1601.04078 [hep-th].
  73. J. J. Heckman, T. Rudelius, and A. Tomasiello, “Fission, Fusion, and 6D RG Flows,” JHEP 02 (2019) 167, arXiv:1807.10274 [hep-th].
  74. N. J. Hitchin, A. Karlhede, U. Lindstrom, and M. Rocek, “Hyperkahler Metrics and Supersymmetry,” Commun. Math. Phys. 108 (1987) 535.
  75. K. Intriligator, “6d, 𝒩=(1, 0)𝒩1 0\mathcal{N}=\left(1,\;0\right)caligraphic_N = ( 1 , 0 ) Coulomb branch anomaly matching,” JHEP 10 (2014) 162, arXiv:1408.6745 [hep-th].
  76. K. A. Intriligator, “New string theories in six-dimensions via branes at orbifold singularities,” Adv. Theor. Math. Phys. 1 (1998) 271–282, arXiv:hep-th/9708117.
  77. Cambridge Monographs on Mathematical Physics. CUP, 1989.
  78. Birkhäuser Boston, Inc., Boston, MA, 1983. https://doi.org/10.1007/978-1-4757-1382-4. An introduction.
  79. M. J. Kang and S. Kang, “Central extensions of higher groups: Green-Schwarz mechanism and 2-connections,” arXiv:2311.14666 [hep-th].
  80. A. Kapustin, “D(n) quivers from branes,” JHEP 12 (1998) 015, arXiv:hep-th/9806238.
  81. N. Mekareeya, K. Ohmori, Y. Tachikawa, and G. Zafrir, “E88{}_{8}start_FLOATSUBSCRIPT 8 end_FLOATSUBSCRIPT instantons on type-A ALE spaces and supersymmetric field theories,” JHEP 09 (2017) 144, arXiv:1707.04370 [hep-th].
  82. N. Mekareeya, T. Rudelius, and A. Tomasiello, “T-branes, Anomalies and Moduli Spaces in 6D SCFTs,” JHEP 10 (2017) 158, arXiv:1612.06399 [hep-th].
  83. D. R. Morrison and W. Taylor, “Classifying bases for 6D F-theory models,” Central Eur. J. Phys. 10 (2012) 1072–1088, arXiv:1201.1943 [hep-th].
  84. D. R. Morrison and C. Vafa, “Compactifications of F theory on Calabi-Yau threefolds. 1,” Nucl. Phys. B 473 (1996) 74–92, arXiv:hep-th/9602114.
  85. D. R. Morrison and C. Vafa, “Compactifications of F theory on Calabi-Yau threefolds. 2.,” Nucl. Phys. B 476 (1996) 437–469, arXiv:hep-th/9603161.
  86. W. Nahm, “Supersymmetries and their Representations,” Nucl. Phys. B 135 (1978) 149.
  87. K. S. Narain, “New Heterotic String Theories in Uncompactified Dimensions <<< 10,” Phys. Lett. B 169 (1986) 41–46.
  88. K. Ohmori, H. Shimizu, and Y. Tachikawa, “Anomaly polynomial of E-string theories,” JHEP 08 (2014) 002, arXiv:1404.3887 [hep-th].
  89. K. Ohmori, H. Shimizu, Y. Tachikawa, and K. Yonekura, “Anomaly polynomial of general 6d SCFTs,” PTEP 2014 no. 10, (2014) 103B07, arXiv:1408.5572 [hep-th].
  90. K. Ohmori, H. Shimizu, Y. Tachikawa, and K. Yonekura, “6d 𝒩=(1,0)𝒩10\mathcal{N}=(1,0)caligraphic_N = ( 1 , 0 ) theories on T2superscript𝑇2T^{2}italic_T start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT and class S theories: Part I,” JHEP 07 (2015) 014, arXiv:1503.06217 [hep-th].
  91. K. Ohmori, H. Shimizu, Y. Tachikawa, and K. Yonekura, “6d 𝒩=(1, 0)𝒩1 0\mathcal{N}=\left(1,\;0\right)caligraphic_N = ( 1 , 0 ) theories on S11{}^{1}start_FLOATSUPERSCRIPT 1 end_FLOATSUPERSCRIPT /T22{}^{2}start_FLOATSUPERSCRIPT 2 end_FLOATSUPERSCRIPT and class S theories: part II,” JHEP 12 (2015) 131, arXiv:1508.00915 [hep-th].
  92. J. Polchinski and E. Witten, “Evidence for heterotic - type I string duality,” Nucl. Phys. B 460 (1996) 525–540, arXiv:hep-th/9510169.
  93. S. S. Razamat, E. Sabag, and G. Zafrir, “From 6d flows to 4d flows,” JHEP 12 (2019) 108, arXiv:1907.04870 [hep-th].
  94. A. Sagnotti, “Open Strings and their Symmetry Groups,” in NATO Advanced Summer Institute on Nonperturbative Quantum Field Theory (Cargese Summer Institute). 9, 1987. arXiv:hep-th/0208020.
  95. N. Seiberg, “New theories in six-dimensions and matrix description of M theory on T**5 and T**5 / Z(2),” Phys. Lett. B 408 (1997) 98–104, arXiv:hep-th/9705221.
  96. N. Seiberg, “Nontrivial fixed points of the renormalization group in six-dimensions,” Phys. Lett. B 390 (1997) 169–171, arXiv:hep-th/9609161.
  97. H. Shimizu, Y. Tachikawa, and G. Zafrir, “Anomaly matching on the Higgs branch,” JHEP 12 (2017) 127, arXiv:1703.01013 [hep-th].
  98. P. Slodowy, Simple singularities and simple algebraic groups. Lecture Notes in Mathematics. Springer-Verlag, 1 ed., 1980.
  99. M. Sperling and Z. Zhong, “Balanced B and D-type orthosymplectic quivers — magnetic quivers for product theories,” JHEP 04 (2022) 145, arXiv:2111.00026 [hep-th].
  100. A. Strominger, “Open p-branes,” Phys. Lett. B 383 (1996) 44–47, arXiv:hep-th/9512059.
  101. T. Weigand, “Lectures on F-theory compactifications and model building,” Class. Quant. Grav. 27 (2010) 214004, arXiv:1009.3497 [hep-th].
  102. E. Witten, “Some comments on string dynamics,” in STRINGS 95: Future Perspectives in String Theory, pp. 501–523. 7, 1995. arXiv:hep-th/9507121.
  103. E. Witten, “Phase transitions in M theory and F theory,” Nucl. Phys. B 471 (1996) 195–216, arXiv:hep-th/9603150.
  104. E. Witten, “Small instantons in string theory,” Nucl. Phys. B 460 (1996) 541–559, arXiv:hep-th/9511030.
Citations (1)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now