$$ \mathcal{N} $$ = 4 superconformal bootstrap of the K _{3} CFT
We study twodimensional (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 4point function. Nontrivial bounds on the nonBPS 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 »
 Authors:

^{[1]};
^{[1]};
^{[2]};
^{[3]};
^{[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:
 Grant/Contract Number:
 SC0009988; FG0291ER40654
 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 10298479
 Publisher:
 Springer Berlin
 Research Org:
 Harvard Univ., Cambridge, MA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC)
 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
 OSTI Identifier:
 1389304
Lin, YingHsuan, Shao, ShuHeng, SimmonsDuffin, David, Wang, Yifan, and Yin, Xi. $ \mathcal{N} $ = 4 superconformal bootstrap of the K3 CFT. United States: N. p.,
Web. doi:10.1007/JHEP05(2017)126.
Lin, YingHsuan, Shao, ShuHeng, SimmonsDuffin, David, Wang, Yifan, & Yin, Xi. $ \mathcal{N} $ = 4 superconformal bootstrap of the K3 CFT. United States. doi:10.1007/JHEP05(2017)126.
Lin, YingHsuan, Shao, ShuHeng, SimmonsDuffin, David, Wang, Yifan, and Yin, Xi. 2017.
"$ \mathcal{N} $ = 4 superconformal bootstrap of the K3 CFT". United States.
doi:10.1007/JHEP05(2017)126. https://www.osti.gov/servlets/purl/1389304.
@article{osti_1389304,
title = {$ \mathcal{N} $ = 4 superconformal bootstrap of the K3 CFT},
author = {Lin, YingHsuan and Shao, ShuHeng and SimmonsDuffin, David and Wang, Yifan and Yin, Xi},
abstractNote = {We study twodimensional (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 4point function. Nontrivial bounds on the nonBPS 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 fourpoint 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 = {2017},
month = {5}
}