$ \mathcal{N} $ = 4 superconformal bootstrap of the K3 CFT

Lin, Ying-Hsuan; Shao, Shu-Heng; Simmons-Duffin, David; Wang, Yifan; Yin, Xi

doi:10.1007/JHEP05(2017)126

Title: $$ \mathcal{N} $$ = 4 superconformal bootstrap of the K₃ CFT

Journal Article · Tue May 23 00:00:00 EDT 2017 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP05(2017)126· OSTI ID:1389304

Lin, Ying-Hsuan ^[1]; Shao, Shu-Heng ^[1]; Simmons-Duffin, David ^[2]; Wang, Yifan ^[3]; Yin, Xi ^[1]

Harvard Univ., Cambridge, MA (United States). Jefferson Physical Lab.
Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics

We study two-dimensional (4; 4) superconformal eld theories of central charge c = 6, corresponding to nonlinear sigma models on K3 surfaces, using the superconformal bootstrap. This is made possible through a surprising relation between the BPS N = 4 superconformal blocks with c = 6 and bosonic Virasoro conformal blocks with c = 28, and an exact result on the moduli dependence of a certain integrated BPS 4-point function. Nontrivial bounds on the non-BPS spectrum in the K3 CFT are obtained as functions of the CFT moduli, that interpolate between the free orbifold points and singular CFT points. We observe directly from the CFT perspective the signature of a continuous spectrum above a gap at the singular moduli, and fi nd numerically an upper bound on this gap that is saturated by the A1 N = 4 cigar CFT. We also derive an analytic upper bound on the fi rst nonzero eigenvalue of the scalar Laplacian on K3 in the large volume regime, that depends on the K3 moduli data. As two byproducts, we find an exact equivalence between a class of BPS N = 2 superconformal blocks and Virasoro conformal blocks in two dimensions, and an upper bound on the four-point functions of operators of sufficiently low scaling dimension in three and four dimensional CFTs.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Harvard Univ., Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0009988; FG02-91ER40654

OSTI ID:: 1389304

Journal Information:: Journal of High Energy Physics (Online), Vol. 2017, Issue 5; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 18 works

Citation information provided by
Web of Science

References (71)

Carving out the space of 4D CFTs Poland, David; Simmons-Duffin, David; Vichi, Alessandro Journal of High Energy Physics, Vol. 2012, Issue 5 https://doi.org/10.1007/JHEP05(2012)110	journal	May 2012
Little string theory in a double scaling limit Giveon, Amit; Kutasov, David Journal of High Energy Physics, Vol. 1999, Issue 10 https://doi.org/10.1088/1126-6708/1999/10/034	journal	October 1999
Little string amplitudes (and the unreasonable effectiveness of 6D SYM) Chang, Chi-Ming; Lin, Ying-Hsuan; Shao, Shu-Heng Journal of High Energy Physics, Vol. 2014, Issue 12 https://doi.org/10.1007/JHEP12(2014)176	journal	December 2014
Causality, analyticity and an IR obstruction to UV completion Adams, Allan; Arkani-Hamed, Nima; Dubovsky, Sergei Journal of High Energy Physics, Vol. 2006, Issue 10 https://doi.org/10.1088/1126-6708/2006/10/014	journal	October 2006
The N = 2 $$ \mathcal{N}=2 $$ superconformal bootstrap Beem, Christopher; Lemos, Madalena; Liendo, Pedro Journal of High Energy Physics, Vol. 2016, Issue 3 https://doi.org/10.1007/JHEP03(2016)183	journal	March 2016
Strings in ${AdS}_{3}$ and the $SL (2, R)$ WZW model. III. Correlation functions Maldacena, Juan; Ooguri, Hirosi Physical Review D, Vol. 65, Issue 10 https://doi.org/10.1103/PhysRevD.65.106006	journal	May 2002
Accidental symmetries and the conformal bootstrap Chester, Shai M.; Giombi, Simone; Iliesiu, Luca V. Journal of High Energy Physics, Vol. 2016, Issue 1 https://doi.org/10.1007/JHEP01(2016)110	journal	January 2016
Bootstrapping the O(N ) vector models Kos, Filip; Poland, David; Simmons-Duffin, David Journal of High Energy Physics, Vol. 2014, Issue 6 https://doi.org/10.1007/JHEP06(2014)091	journal	June 2014
Causality constraints in conformal field theory Hartman, Thomas; Jain, Sachin; Kundu, Sandipan Journal of High Energy Physics, Vol. 2016, Issue 5 https://doi.org/10.1007/JHEP05(2016)099	journal	May 2016
N $$ \mathcal{N} $$ = 1 superconformal blocks for general scalar operators Khandker, Zuhair U.; Li, Daliang; Poland, David Journal of High Energy Physics, Vol. 2014, Issue 8 https://doi.org/10.1007/JHEP08(2014)049	journal	August 2014
Orbifolds and solitons Kutasov, D. Physics Letters B, Vol. 383, Issue 1 https://doi.org/10.1016/0370-2693(96)00708-3	journal	August 1996
Supersymmetry Constraints and String Theory on K3 Lin, Ying-Hsuan; Shao, Shu-Heng; Wang, Yifan Journal of High Energy Physics, Vol. 2015, Issue 12 https://doi.org/10.1007/JHEP12(2015)142	journal	December 2015
On the Liouville three-point function Teschner, Jörg Physics Letters B, Vol. 363, Issue 1-2 https://doi.org/10.1016/0370-2693(95)01200-A	journal	November 1995
A Hiker's Guide to K3.¶Aspects of N= (4,4) Superconformal Field Theory¶with Central Charge c= 6 Nahm, Werner; Wendland, Katrin Communications in Mathematical Physics, Vol. 216, Issue 1 https://doi.org/10.1007/PL00005548	journal	January 2001
Current algebra and Wess-Zumino model in two dimensions Knizhnik, V. G.; Zamolodchikov, A. B. Nuclear Physics B, Vol. 247, Issue 1 https://doi.org/10.1016/0550-3213(84)90374-2	journal	December 1984
Character formulas for the N = 4 superconformal algebra Eguchi, Tohru; Taormina, Anne Physics Letters B, Vol. 200, Issue 3 https://doi.org/10.1016/0370-2693(88)90778-2	journal	January 1988
Two-dimensional black hole and singularities of CY manifolds Ooguri, Hirosi; Vafa, Cumrun Nuclear Physics B, Vol. 463, Issue 1 https://doi.org/10.1016/0550-3213(96)00008-9	journal	March 1996
Ale Manifolds and Conformal Field Theories Anselmi, Damiano; BillÓ, Marco; FrÉ, Pietro International Journal of Modern Physics A, Vol. 09, Issue 17 https://doi.org/10.1142/S0217751X94001199	journal	July 1994
Duality in quantum field theory Mack, G. Nuclear Physics B, Vol. 118, Issue 5 https://doi.org/10.1016/0550-3213(77)90238-3	journal	February 1977
Liouville theory revisited Teschner, J. Classical and Quantum Gravity, Vol. 18, Issue 23 https://doi.org/10.1088/0264-9381/18/23/201	journal	November 2001
Modular Constraints on Calabi-Yau Compactifications Keller, Christoph A.; Ooguri, Hirosi Communications in Mathematical Physics, Vol. 324, Issue 1 https://doi.org/10.1007/s00220-013-1797-8	journal	September 2013
The Theory of the Double Gamma Function Barnes, E. W. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 196, Issue 274-286 https://doi.org/10.1098/rsta.1901.0006	journal	January 1901
Operator product expansion and factorization in the H3+-WZNW model Teschner, J. Nuclear Physics B, Vol. 571, Issue 3 https://doi.org/10.1016/S0550-3213(99)00785-3	journal	April 2000
A semidefinite program solver for the conformal bootstrap Simmons-Duffin, David Journal of High Energy Physics, Vol. 2015, Issue 6 https://doi.org/10.1007/JHEP06(2015)174	journal	June 2015
Numerical Calabi–Yau metrics Douglas, Michael R.; Karp, Robert L.; Lukic, Sergio Journal of Mathematical Physics, Vol. 49, Issue 3 https://doi.org/10.1063/1.2888403	journal	March 2008
Tensor representations of conformal algebra and conformally covariant operator product expansion Ferrara, S.; Grillo, A. F.; Gatto, R. Annals of Physics, Vol. 76, Issue 1 https://doi.org/10.1016/0003-4916(73)90446-6	journal	March 1973
Symmetries of K3 sigma models Gaberdiel, Matthias R.; Hohenegger, Stefan; Volpato, Roberto Communications in Number Theory and Physics, Vol. 6, Issue 1 https://doi.org/10.4310/CNTP.2012.v6.n1.a1	journal	January 2012
Topological—anti-topological fusion Cecotti, Sergio; Vafa, Cumrun Nuclear Physics B, Vol. 367, Issue 2 https://doi.org/10.1016/0550-3213(91)90021-O	journal	December 1991
Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$ c -Minimization and Precise Critical Exponents El-Showk, Sheer; Paulos, Miguel F.; Poland, David Journal of Statistical Physics, Vol. 157, Issue 4-5 https://doi.org/10.1007/s10955-014-1042-7	journal	June 2014
Bootstrapping 3D fermions Iliesiu, Luca; Kos, Filip; Poland, David Journal of High Energy Physics, Vol. 2016, Issue 3 https://doi.org/10.1007/JHEP03(2016)120	journal	March 2016
Conformal bootstrap in Liouville field theory Zamolodchikov, A.; Zamolodchikov, Al. Nuclear Physics B, Vol. 477, Issue 2 https://doi.org/10.1016/0550-3213(96)00351-3	journal	October 1996
A K3 sigma model with $ \mathbb{Z}_2^8 $ : $ {{\mathbb{M}}_{20 }} $ symmetry Gaberdiel, Matthias R.; Taormina, Anne; Volpato, Roberto Journal of High Energy Physics, Vol. 2014, Issue 2 https://doi.org/10.1007/JHEP02(2014)022	journal	February 2014
String theory on group manifolds Gepner, Doron; Witten, Edward Nuclear Physics B, Vol. 278, Issue 3 https://doi.org/10.1016/0550-3213(86)90051-9	journal	December 1986
Bootstrapping the O(N) archipelago Kos, Filip; Poland, David; Simmons-Duffin, David Journal of High Energy Physics, Vol. 2015, Issue 11 https://doi.org/10.1007/JHEP11(2015)106	journal	November 2015
N=2 Landau-Ginzburg vs. Calabi-Yau σ-Models: Non-Perturbative Aspects Cecotti, S. International Journal of Modern Physics A, Vol. 06, Issue 10 https://doi.org/10.1142/S0217751X91000939	journal	April 1991
Conifold Type Singularities, N =2 Liouville and SL(2;R)/U(1) Theories Eguchi, Tohru; Sugawara, Yuji Journal of High Energy Physics, Vol. 2005, Issue 01 https://doi.org/10.1088/1126-6708/2005/01/027	journal	January 2005
Enhanced gauge symmetries and K3 surfaces Aspinwall, Paul S. Physics Letters B, Vol. 357, Issue 3 https://doi.org/10.1016/0370-2693(95)00957-M	journal	September 1995
Observations on the moduli space of superconformal field theories Seiberg, Nathan Nuclear Physics B, Vol. 303, Issue 2 https://doi.org/10.1016/0550-3213(88)90183-6	journal	June 1988
On structure constants and fusion rules in the model Teschner, J. Nuclear Physics B, Vol. 546, Issue 1-2 https://doi.org/10.1016/S0550-3213(99)00072-3	journal	April 1999
Bounding the heat trace of a Calabi-Yau manifold Fiset, Marc-Antoine; Walcher, Johannes Journal of High Energy Physics, Vol. 2015, Issue 9 https://doi.org/10.1007/JHEP09(2015)124	journal	September 2015
Non-BPS states in heterotic-type IIA duality Bergman, Oren; Gaberdiel, Matthias R. Journal of High Energy Physics, Vol. 1999, Issue 03 https://doi.org/10.1088/1126-6708/1999/03/013	journal	March 1999
Bounds on 4D conformal and superconformal field theories Poland, David; Simmons-Duffin, David Journal of High Energy Physics, Vol. 2011, Issue 5 https://doi.org/10.1007/JHEP05(2011)017	journal	May 2011
A universal inequality for CFT and quantum gravity Hellerman, Simeon Journal of High Energy Physics, Vol. 2011, Issue 8 https://doi.org/10.1007/JHEP08(2011)130	journal	August 2011
The conformal field theory of orbifolds Dixon, Lance; Friedan, Daniel; Martinec, Emil Nuclear Physics B, Vol. 282 https://doi.org/10.1016/0550-3213(87)90676-6	journal	January 1987
Elliptic genera of ALE and ALF manifolds from gauged linear sigma models Harvey, Jeffrey A.; Lee, Sungjay; Murthy, Sameer Journal of High Energy Physics, Vol. 2015, Issue 2 https://doi.org/10.1007/JHEP02(2015)110	journal	February 2015
Reflections on conformal spectra Kim, Hyungrok; Kravchuk, Petr; Ooguri, Hirosi Journal of High Energy Physics, Vol. 2016, Issue 4 https://doi.org/10.1007/JHEP04(2016)184	journal	April 2016
Heterotic/type II triality and instantons on K ₃ Kiritsis, Elias; Obers, Niels; Pioline, Boris Journal of High Energy Physics, Vol. 2000, Issue 01 https://doi.org/10.1088/1126-6708/2000/01/029	journal	January 2000
Looking for a bulk point Maldacena, Juan; Simmons-Duffin, David; Zhiboedov, Alexander Journal of High Energy Physics, Vol. 2017, Issue 1 https://doi.org/10.1007/JHEP01(2017)013	journal	January 2017
Eigenfunctions and eigenvalues of Laplacian Cheng, Shiu Yuen Differential Geometry, Part 2 https://doi.org/10.1090/pspum/027.2/0378003	book	January 1975
Energy functionals for Calabi-Yau metrics Headrick, Matthew; Nassar, Ali Advances in Theoretical and Mathematical Physics, Vol. 17, Issue 5 https://doi.org/10.4310/ATMP.2013.v17.n5.a1	journal	January 2013
Bounding scalar operator dimensions in 4 D CFT Rattazzi, Riccardo; Rychkov, Vyacheslav S.; Tonni, Erik Journal of High Energy Physics, Vol. 2008, Issue 12 https://doi.org/10.1088/1126-6708/2008/12/031	journal	December 2008
$N = 4$ Superconformal Bootstrap Beem, Christopher; Rastelli, Leonardo; van Rees, Balt C. Physical Review Letters, Vol. 111, Issue 7 https://doi.org/10.1103/PhysRevLett.111.071601	journal	August 2013
Comments on the N = 2,3,4 superconformal algebras in two dimensions Schwimmer, A.; Seiberg, N. Physics Letters B, Vol. 184, Issue 2-3 https://doi.org/10.1016/0370-2693(87)90566-1	journal	January 1987
Unitary representations of the N=4 superconformal algebra Eguchi, Tohru; Taormina, Anne Physics Letters B, Vol. 196, Issue 1 https://doi.org/10.1016/0370-2693(87)91679-0	journal	September 1987
N = 2 strings on orbifolds Glück, Dan; Oz, Yaron; Sakai, Tadakatsu Journal of High Energy Physics, Vol. 2005, Issue 08 https://doi.org/10.1088/1126-6708/2005/08/008	journal	August 2005
Exact correlators of BPS Operators from the 3d superconformal bootstrap Chester, Shai M.; Lee, Jaehoon; Pufu, Silviu S. Journal of High Energy Physics, Vol. 2015, Issue 3 https://doi.org/10.1007/JHEP03(2015)130	journal	March 2015
The N = 8 $$ \mathcal{N}=8 $$ superconformal bootstrap in three dimensions Chester, Shai M.; Lee, Jaehoon; Pufu, Silviu S. Journal of High Energy Physics, Vol. 2014, Issue 9 https://doi.org/10.1007/JHEP09(2014)143	journal	September 2014
Space-time supersymmetry in compactified string theory and superconformal models Gepner, Doron Nuclear Physics B, Vol. 296, Issue 4 https://doi.org/10.1016/0550-3213(88)90397-5	journal	January 1988
Bootstrapping N = 2 $$ \mathcal{N}=2 $$ chiral correlators Lemos, Madalena; Liendo, Pedro Journal of High Energy Physics, Vol. 2016, Issue 1 https://doi.org/10.1007/JHEP01(2016)025	journal	January 2016
C=1 conformal field theories on Riemann surfaces Dijkgraaf, Robbert; Verlinde, Erik; Verlinde, Herman Communications in Mathematical Physics, Vol. 115, Issue 4 https://doi.org/10.1007/BF01224132	journal	December 1988
Covariant approaches to superconformal blocks Fitzpatrick, A. Liam; Kaplan, Jared; Khandker, Zuhair U. Journal of High Energy Physics, Vol. 2014, Issue 8 https://doi.org/10.1007/JHEP08(2014)129	journal	August 2014
On the unitary representations of N=2 and N=4 superconformal algebras Eguchi, Tohru; Taormina, Anne Physics Letters B, Vol. 210, Issue 1-2 https://doi.org/10.1016/0370-2693(88)90360-7	journal	August 1988
Infinite conformal symmetry in two-dimensional quantum field theory Belavin, A. A.; Polyakov, A. M.; Zamolodchikov, A. B. Nuclear Physics B, Vol. 241, Issue 2 https://doi.org/10.1016/0550-3213(84)90052-X	journal	July 1984
topological amplitudes and string effective action Antoniadis, I.; Hohenegger, S.; Narain, K. S. Nuclear Physics B, Vol. 771, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2007.02.011	journal	May 2007
Superconformal algebras and string compactification on manifolds with SU(n) holonomy Eguchi, Tohru; Ooguri, Hirosi; Taormina, Anne Nuclear Physics B, Vol. 315, Issue 1 https://doi.org/10.1016/0550-3213(89)90454-9	journal	March 1989
H ₃ ⁺ -WZNW correlators from Liouville theory Ribault, Sylvain; Teschner, Joerg Journal of High Energy Physics, Vol. 2005, Issue 06 https://doi.org/10.1088/1126-6708/2005/06/014	journal	June 2005
Bounds on OPE coefficients in 4D Conformal Field Theories Caracciolo, Francesco; Echeverri, Alejandro Castedo; von Harling, Benedict Journal of High Energy Physics, Vol. 2014, Issue 10 https://doi.org/10.1007/JHEP10(2014)020	journal	October 2014
A non-renormalization theorem for chiral primary 3-point functions Baggio, Marco; de Boer, Jan; Papadodimas, Kyriakos Journal of High Energy Physics, Vol. 2012, Issue 7 https://doi.org/10.1007/JHEP07(2012)137	journal	July 2012
Bootstrapping mixed correlators in the 3D Ising model Kos, Filip; Poland, David; Simmons-Duffin, David Journal of High Energy Physics, Vol. 2014, Issue 11 https://doi.org/10.1007/JHEP11(2014)109	journal	November 2014
Duality of the fermionic 2d black hole and N = 2 Liouville theory as mirror symmetry Hori, Kentaro; Kapustin, Anton Journal of High Energy Physics, Vol. 2001, Issue 08 https://doi.org/10.1088/1126-6708/2001/08/045	journal	August 2001
Conformal symmetry in two dimensions: An explicit recurrence formula for the conformal partial wave amplitude Zamolodchikov, Al. B. Communications in Mathematical Physics, Vol. 96, Issue 3 https://doi.org/10.1007/BF01214585	journal	September 1984

Cited By (13)

Inverse bootstrapping conformal field theories Li, Wenliang Journal of High Energy Physics, Vol. 2018, Issue 1 https://doi.org/10.1007/jhep01(2018)077	journal	January 2018
Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds Bossard, Guillaume; Cosnier-Horeau, Charles; Pioline, Boris SciPost Physics, Vol. 7, Issue 3 https://doi.org/10.21468/scipostphys.7.3.028	journal	January 2019
Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory Cornagliotto, Martina; Lemos, Madalena; Liendo, Pedro Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-11690	text	January 2017
Long multiplet bootstrap Cornagliotto, Martina; Lemos, Madalena; Schomerus, Volker Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-11762	text	January 2017
Bootstrapping the Spectral Function: On the Uniqueness of Liouville and the Universality of BTZ Collier, Scott; Kravchuk, Petr; Lin, Ying-Hsuan arXiv https://doi.org/10.48550/arxiv.1702.00423	text	January 2017
Weight Shifting Operators and Conformal Blocks Karateev, Denis; Kravchuk, Petr; Simmons-Duffin, David arXiv https://doi.org/10.48550/arxiv.1706.07813	text	January 2017
The 3d Stress-Tensor Bootstrap Dymarsky, Anatoly; Kos, Filip; Kravchuk, Petr arXiv https://doi.org/10.48550/arxiv.1708.05718	text	January 2017
Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey Chang, Chi-Ming; Fluder, Martin; Lin, Ying-Hsuan arXiv https://doi.org/10.48550/arxiv.1710.08418	text	January 2017
Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory Cornagliotto, Martina; Lemos, Madalena; Liendo, Pedro arXiv https://doi.org/10.48550/arxiv.1711.00016	text	January 2017
Solving M-theory with the Conformal Bootstrap Agmon, Nathan B.; Chester, Shai M.; Pufu, Silviu S. arXiv https://doi.org/10.48550/arxiv.1711.07343	text	January 2017
The Conformal Bootstrap: Theory, Numerical Techniques, and Applications Poland, David; Rychkov, Slava; Vichi, Alessandro arXiv https://doi.org/10.48550/arxiv.1805.04405	text	January 2018
Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds Bossard, Guillaume; Cosnier-Horeau, Charles; Pioline, Boris arXiv https://doi.org/10.48550/arxiv.1806.03330	text	January 2018
Large $c$ Virasoro Blocks from Monodromy Method beyond Known Limits Kusuki, Yuya arXiv https://doi.org/10.48550/arxiv.1806.04352	text	January 2018

Similar Records

(2, 2) superconformal bootstrap in two dimensions

Journal Article · Fri May 19 00:00:00 EDT 2017 · Journal of High Energy Physics (Online) · OSTI ID:1389304

Lin, Ying -Hsuan; Shao, Shu -Heng; Wang, Yifan; +1 more

Quantum Regge trajectories and the Virasoro analytic bootstrap

Journal Article · Fri May 31 00:00:00 EDT 2019 · Journal of High Energy Physics (Online) · OSTI ID:1389304

Collier, Scott; Gobeil, Yan; Maxfield, Henry; +1 more

Moonshine, superconformal symmetry, and quantum error correction

Journal Article · Wed May 27 00:00:00 EDT 2020 · Journal of High Energy Physics (Online) · OSTI ID:1389304

Harvey, Jeffrey A.; Moore, Gregory W.

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Conformal Field Theory
Extended Supersymmetry
Field Theories in Lower Dimensions

Title: $$ \mathcal{N} $$ = 4 superconformal bootstrap of the K3 CFT

Citation Formats

References (71)

Cited By (13)

Similar Records

Related Subjects

Title: $$ \mathcal{N} $$ = 4 superconformal bootstrap of the K₃ CFT