$ \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

Abstract

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 boundmore »« less

Authors:

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

Publication Date:: Tue May 23 00:00:00 EDT 2017

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

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1389304

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

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 5; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

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

Citation Formats


                    Lin, Ying-Hsuan, Shao, Shu-Heng, Simmons-Duffin, David, Wang, Yifan, and Yin, Xi. $ \mathcal{N} $ = 4 superconformal bootstrap of the K3 CFT.  United States: N. p., 2017. 
Web.  doi:10.1007/JHEP05(2017)126.

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                    Lin, Ying-Hsuan, Shao, Shu-Heng, Simmons-Duffin, David, Wang, Yifan, & Yin, Xi. $ \mathcal{N} $ = 4 superconformal bootstrap of the K3 CFT.  United States.  https://doi.org/10.1007/JHEP05(2017)126

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                    Lin, Ying-Hsuan, Shao, Shu-Heng, Simmons-Duffin, David, Wang, Yifan, and Yin, Xi. Tue .  
"$ \mathcal{N} $ = 4 superconformal bootstrap of the K3 CFT".  United States.  https://doi.org/10.1007/JHEP05(2017)126.  https://www.osti.gov/servlets/purl/1389304.

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@article{osti_1389304,

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

  author       = {Lin, Ying-Hsuan and Shao, Shu-Heng and Simmons-Duffin, David and Wang, Yifan and Yin, Xi},

  abstractNote = {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.},

  doi          = {10.1007/JHEP05(2017)126},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 5,

  volume       = 2017,

  place        = {United States},

  year         = {Tue May 23 00:00:00 EDT 2017},

  month        = {Tue May 23 00:00:00 EDT 2017}

}

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https://doi.org/10.1007/JHEP07(2020)065

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BPS Wilson loop in $$\mathcal{N}$$ = 2 superconformal SU(N) “orientifold” gauge theory and weak-strong coupling interpolation

Journal Article Beccaria, M. ; Dunne, G. V. ; Tseytlin, A. A. - Journal of High Energy Physics (Online)

We consider the expectation value $ \left\langle \mathcal{W}\right\rangle $ of the circular BPS Wilson loop in $ \mathcal{N} $ = 2 superconformal SU(N) gauge theory containing a vector multiplet coupled to two hypermultiplets in rank-2 symmetric and antisymmetric representations. This theory admits a regular large N expansion, is planar-equivalent to $ \mathcal{N} $ = 4 SYM theory and is expected to be dual to a certain orbifold/orientifold projection of AdS₅ × S⁵ superstring theory. On the string theory side $ \left\langle \mathcal{W}\right\rangle $ is represented by the path integral expanded near the same AdS₂ minimal surface as in the maximallymore »« less
https://doi.org/10.1007/jhep07(2021)085

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

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Carving out the space of 4D CFTs journal, May 2012

Little string theory in a double scaling limit journal, October 1999

Little string amplitudes (and the unreasonable effectiveness of 6D SYM) journal, December 2014

Causality, analyticity and an IR obstruction to UV completion journal, October 2006

The N = 2 $$ \mathcal{N}=2 $$ superconformal bootstrap journal, March 2016

Strings in AdS 3 and the SL ( 2 , R ) WZW model. III. Correlation functions journal, May 2002

Accidental symmetries and the conformal bootstrap journal, January 2016

Bootstrapping the O(N ) vector models journal, June 2014

Causality constraints in conformal field theory journal, May 2016

N $$ \mathcal{N} $$ = 1 superconformal blocks for general scalar operators journal, August 2014

Orbifolds and solitons journal, August 1996

Supersymmetry Constraints and String Theory on K3 journal, December 2015

On the Liouville three-point function journal, November 1995

A Hiker's Guide to K3.¶Aspects of N= (4,4) Superconformal Field Theory¶with Central Charge c= 6 journal, January 2001

Current algebra and Wess-Zumino model in two dimensions journal, December 1984

Character formulas for the N = 4 superconformal algebra journal, January 1988

Two-dimensional black hole and singularities of CY manifolds journal, March 1996

Ale Manifolds and Conformal Field Theories journal, July 1994

Duality in quantum field theory journal, February 1977

Liouville theory revisited journal, November 2001

Modular Constraints on Calabi-Yau Compactifications journal, September 2013

The Theory of the Double Gamma Function journal, January 1901

Operator product expansion and factorization in the H3+-WZNW model journal, April 2000

A semidefinite program solver for the conformal bootstrap journal, June 2015

Numerical Calabi–Yau metrics journal, March 2008

Tensor representations of conformal algebra and conformally covariant operator product expansion journal, March 1973

Symmetries of K3 sigma models journal, January 2012

Topological—anti-topological fusion journal, December 1991

Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$ c -Minimization and Precise Critical Exponents journal, June 2014

Bootstrapping 3D fermions journal, March 2016

Conformal bootstrap in Liouville field theory journal, October 1996

A K3 sigma model with $ \mathbb{Z}_2^8 $ : $ {{\mathbb{M}}_{20 }} $ symmetry journal, February 2014

String theory on group manifolds journal, December 1986

Bootstrapping the O(N) archipelago journal, November 2015

N=2 Landau-Ginzburg vs. Calabi-Yau σ-Models: Non-Perturbative Aspects journal, April 1991

Conifold Type Singularities, N =2 Liouville and SL(2;R)/U(1) Theories journal, January 2005

Enhanced gauge symmetries and K3 surfaces journal, September 1995

Observations on the moduli space of superconformal field theories journal, June 1988

On structure constants and fusion rules in the model journal, April 1999

Bounding the heat trace of a Calabi-Yau manifold journal, September 2015

Non-BPS states in heterotic-type IIA duality journal, March 1999

Bounds on 4D conformal and superconformal field theories journal, May 2011

A universal inequality for CFT and quantum gravity journal, August 2011

The conformal field theory of orbifolds journal, January 1987

Elliptic genera of ALE and ALF manifolds from gauged linear sigma models journal, February 2015

Reflections on conformal spectra journal, April 2016

Heterotic/type II triality and instantons on K 3 journal, January 2000

Looking for a bulk point journal, January 2017

Eigenfunctions and eigenvalues of Laplacian book, January 1975

Energy functionals for Calabi-Yau metrics journal, January 2013

Bounding scalar operator dimensions in 4 D CFT journal, December 2008

N = 4 Superconformal Bootstrap journal, August 2013

Comments on the N = 2,3,4 superconformal algebras in two dimensions journal, January 1987

Unitary representations of the N=4 superconformal algebra journal, September 1987

N = 2 strings on orbifolds journal, August 2005

Exact correlators of BPS Operators from the 3d superconformal bootstrap journal, March 2015

The N = 8 $$ \mathcal{N}=8 $$ superconformal bootstrap in three dimensions journal, September 2014

Space-time supersymmetry in compactified string theory and superconformal models journal, January 1988

Bootstrapping N = 2 $$ \mathcal{N}=2 $$ chiral correlators journal, January 2016

C=1 conformal field theories on Riemann surfaces journal, December 1988

Covariant approaches to superconformal blocks journal, August 2014

On the unitary representations of N=2 and N=4 superconformal algebras journal, August 1988

Infinite conformal symmetry in two-dimensional quantum field theory journal, July 1984

topological amplitudes and string effective action journal, May 2007

Superconformal algebras and string compactification on manifolds with SU(n) holonomy journal, March 1989

H 3 + -WZNW correlators from Liouville theory journal, June 2005

Bounds on OPE coefficients in 4D Conformal Field Theories journal, October 2014

A non-renormalization theorem for chiral primary 3-point functions journal, July 2012

Bootstrapping mixed correlators in the 3D Ising model journal, November 2014

Duality of the fermionic 2d black hole and N = 2 Liouville theory as mirror symmetry journal, August 2001

Conformal symmetry in two dimensions: An explicit recurrence formula for the conformal partial wave amplitude journal, September 1984

Inverse bootstrapping conformal field theories journal, January 2018

Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds journal, January 2019

Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory text, January 2017

Long multiplet bootstrap text, January 2017

Bootstrapping the Spectral Function: On the Uniqueness of Liouville and the Universality of BTZ text, January 2017

Weight Shifting Operators and Conformal Blocks text, January 2017

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

Carving out the space of 4D CFTs
journal, May 2012

Little string theory in a double scaling limit
journal, October 1999

Little string amplitudes (and the unreasonable effectiveness of 6D SYM)
journal, December 2014

Causality, analyticity and an IR obstruction to UV completion
journal, October 2006

The N = 2 $$ \mathcal{N}=2 $$ superconformal bootstrap
journal, March 2016

Strings in ${AdS}_{3}$ and the $SL (2, R)$ WZW model. III. Correlation functions
journal, May 2002

Accidental symmetries and the conformal bootstrap
journal, January 2016

Bootstrapping the O(N ) vector models
journal, June 2014

Causality constraints in conformal field theory
journal, May 2016

N $$ \mathcal{N} $$ = 1 superconformal blocks for general scalar operators
journal, August 2014

Orbifolds and solitons
journal, August 1996

Supersymmetry Constraints and String Theory on K3
journal, December 2015

On the Liouville three-point function
journal, November 1995

A Hiker's Guide to K3.¶Aspects of N= (4,4) Superconformal Field Theory¶with Central Charge c= 6
journal, January 2001

Current algebra and Wess-Zumino model in two dimensions
journal, December 1984

Character formulas for the N = 4 superconformal algebra
journal, January 1988

Two-dimensional black hole and singularities of CY manifolds
journal, March 1996

Ale Manifolds and Conformal Field Theories
journal, July 1994

Duality in quantum field theory
journal, February 1977

Liouville theory revisited
journal, November 2001

Modular Constraints on Calabi-Yau Compactifications
journal, September 2013

The Theory of the Double Gamma Function
journal, January 1901

Operator product expansion and factorization in the H3+-WZNW model
journal, April 2000

A semidefinite program solver for the conformal bootstrap
journal, June 2015

Numerical Calabi–Yau metrics
journal, March 2008

Tensor representations of conformal algebra and conformally covariant operator product expansion
journal, March 1973

Symmetries of K3 sigma models
journal, January 2012

Topological—anti-topological fusion
journal, December 1991

Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$ c -Minimization and Precise Critical Exponents
journal, June 2014

Bootstrapping 3D fermions
journal, March 2016

Conformal bootstrap in Liouville field theory
journal, October 1996

A K3 sigma model with $ \mathbb{Z}_2^8 $ : $ {{\mathbb{M}}_{20 }} $ symmetry
journal, February 2014

String theory on group manifolds
journal, December 1986

Bootstrapping the O(N) archipelago
journal, November 2015

N=2 Landau-Ginzburg vs. Calabi-Yau σ-Models: Non-Perturbative Aspects
journal, April 1991

Conifold Type Singularities, N =2 Liouville and SL(2;R)/U(1) Theories
journal, January 2005

Enhanced gauge symmetries and K3 surfaces
journal, September 1995

Observations on the moduli space of superconformal field theories
journal, June 1988

On structure constants and fusion rules in the model
journal, April 1999

Bounding the heat trace of a Calabi-Yau manifold
journal, September 2015

Non-BPS states in heterotic-type IIA duality
journal, March 1999

Bounds on 4D conformal and superconformal field theories
journal, May 2011

A universal inequality for CFT and quantum gravity
journal, August 2011

The conformal field theory of orbifolds
journal, January 1987

Elliptic genera of ALE and ALF manifolds from gauged linear sigma models
journal, February 2015

Reflections on conformal spectra
journal, April 2016

Heterotic/type II triality and instantons on K ₃
journal, January 2000

Looking for a bulk point
journal, January 2017

Eigenfunctions and eigenvalues of Laplacian
book, January 1975

Energy functionals for Calabi-Yau metrics
journal, January 2013

Bounding scalar operator dimensions in 4 D CFT
journal, December 2008

$N = 4$ Superconformal Bootstrap
journal, August 2013

Comments on the N = 2,3,4 superconformal algebras in two dimensions
journal, January 1987

Unitary representations of the N=4 superconformal algebra
journal, September 1987

N = 2 strings on orbifolds
journal, August 2005

Exact correlators of BPS Operators from the 3d superconformal bootstrap
journal, March 2015

The N = 8 $$ \mathcal{N}=8 $$ superconformal bootstrap in three dimensions
journal, September 2014

Space-time supersymmetry in compactified string theory and superconformal models
journal, January 1988

Bootstrapping N = 2 $$ \mathcal{N}=2 $$ chiral correlators
journal, January 2016

C=1 conformal field theories on Riemann surfaces
journal, December 1988

Covariant approaches to superconformal blocks
journal, August 2014

On the unitary representations of N=2 and N=4 superconformal algebras
journal, August 1988

Infinite conformal symmetry in two-dimensional quantum field theory
journal, July 1984

topological amplitudes and string effective action
journal, May 2007

Superconformal algebras and string compactification on manifolds with SU(n) holonomy
journal, March 1989

H ₃ ⁺ -WZNW correlators from Liouville theory
journal, June 2005

Bounds on OPE coefficients in 4D Conformal Field Theories
journal, October 2014

A non-renormalization theorem for chiral primary 3-point functions
journal, July 2012

Bootstrapping mixed correlators in the 3D Ising model
journal, November 2014

Duality of the fermionic 2d black hole and N = 2 Liouville theory as mirror symmetry
journal, August 2001

Conformal symmetry in two dimensions: An explicit recurrence formula for the conformal partial wave amplitude
journal, September 1984

Inverse bootstrapping conformal field theories
journal, January 2018

Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds
journal, January 2019

Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory
text, January 2017

Long multiplet bootstrap
text, January 2017

Bootstrapping the Spectral Function: On the Uniqueness of Liouville and the Universality of BTZ
text, January 2017

Weight Shifting Operators and Conformal Blocks
text, January 2017

The 3d Stress-Tensor Bootstrap
text, January 2017

Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey
text, January 2017