Modular bootstrap revisited Collier, Scott; Lin, Ying-Hsuan; Yin, Xi
The journal of high energy physics,
09/2018, Letnik:
2018, Številka:
9
Journal Article
Recenzirano
Odprti dostop
A
bstract
We constrain the spectrum of two-dimensional unitary, compact conformal field theories with central charge
c >
1 using modular bootstrap. Upper bounds on the gap in the dimension of primary ...operators of any spin, as well as in the dimension of scalar primaries, are computed numerically as functions of the central charge using semi-definite programming. Our bounds refine those of Hellerman and Friedan-Keller, and are in some cases saturated by known CFTs. In particular, we show that unitary CFTs with
c <
8 must admit relevant deformations, and that a nontrivial bound on the gap of scalar primaries exists for
c <
25. We also study bounds on the dimension gap in the presence of twist gaps, bounds on the degeneracy of operators, and demonstrate how “extremal spectra” which maximize the degeneracy at the gap can be determined numerically.
A
bstract
We construct the defining data of two-dimensional topological field theories (TFTs) enriched by non-invertible symmetries/topological defect lines. Simple formulae for the three-point ...functions and the lasso two-point functions are derived, and crossing symmetry is proven. The key ingredients are open-to-closed maps and a boundary crossing relation, by which we show that a diagonal basis exists in the defect Hilbert spaces. We then introduce regular TFTs, provide their explicit constructions for the Fibonacci, Ising and Haagerup ℋ
3
fusion categories, and match our formulae with previous bootstrap results. We end by explaining how non-regular TFTs are obtained from regular TFTs via generalized gauging.
Holomorphic modular bootstrap revisited Kaidi, Justin; Lin, Ying-Hsuan; Parra-Martinez, Julio
The journal of high energy physics,
12/2021, Letnik:
2021, Številka:
12
Journal Article
Recenzirano
Odprti dostop
A
bstract
In this work we revisit the “holomorphic modular bootstrap”, i.e. the classification of rational conformal field theories via an analysis of the modular differential equations satisfied by ...their characters. By making use of the representation theory of PSL(2
,
ℤ
n
), we describe a method to classify allowed central charges and weights (
c, h
i
) for theories with any number of characters
d
. This allows us to avoid various bottlenecks encountered previously in the literature, and leads to a classification of consistent characters up to
d
= 5 whose modular differential equations are uniquely fixed in terms of (
c, h
i
). In the process, we identify the full set of constraints on the allowed values of the Wronskian index for fixed
d ≤
5.
A
bstract
It is known that the asymptotic density of states of a 2d CFT in an irreducible representation
ρ
of a finite symmetry group
G
is proportional to (dim
ρ
)
2
. We show how this statement can ...be generalized when the symmetry can be non-invertible and is described by a fusion category
C
. Along the way, we explain what plays the role of a representation of a group in the case of a fusion category symmetry; the answer to this question is already available in the broader mathematical physics literature but not yet widely known in hep-th. This understanding immediately implies a selection rule on the correlation functions, and also allows us to derive the asymptotic density.
A
bstract
We investigate the emergence of topological defect lines in the conformal Regge limit of two-dimensional conformal field theory. We explain how a local operator can be factorized into a ...holomorphic and an anti-holomorphic defect operator connected through a topological defect line, and discuss implications on analyticity and Lorentzian dynamics including aspects of chaos. We derive a formula relating the infinite boost limit, which holographically encodes the “opacity” of bulk scattering, to the action of topological defect lines on local operators. Leveraging the unitary bound on the opacity and the positivity of fusion coefficients, we show that the spectral radii of a large class of topological defect lines are given by their loop expectation values. Factorization also gives a formula relating the local and defect operator algebras and fusion categorical data. We then review factorization in rational conformal field theory from a defect perspective, and examine irrational theories. On the orbifold branch of the
c
= 1 free boson theory, we find a unified description for the topological defect lines through which the twist fields are factorized; at irrational points, the twist fields factorize through “non-compact” topological defect lines which exhibit continuous defect operator spectra. Along the way, we initiate the development of a formalism to characterize non-compact topological defect lines.
A
bstract
We consider topological defect lines (TDLs) in two-dimensional conformal field theories. Generalizing and encompassing both global symmetries and Verlinde lines, TDLs together with their ...attached defect operators provide models of fusion categories without braiding. We study the crossing relations of TDLs, discuss their relation to the ’t Hooft anomaly, and use them to constrain renormalization group flows to either conformal critical points or topological quantum field theories (TQFTs). We show that if certain non-invertible TDLs are preserved along a RG flow, then the vacuum cannot be a non-degenerate gapped state. For various massive flows, we determine the infrared TQFTs completely from the consideration of TDLs together with modular invariance.
A
bstract
We introduce spectral functions that capture the distribution of OPE coefficients and density of states in two-dimensional conformal field theories, and show that nontrivial upper and lower ...bounds on the spectral function can be obtained from semidefinite programming. We find substantial numerical evidence indicating that OPEs involving only scalar Virasoro primaries in a
c >
1 CFT are necessarily governed by the structure constants of Liouville theory. Combining this with analytic results in modular bootstrap, we conjecture that Liouville theory is the unique unitary
c >
1 CFT whose primaries have bounded spins. We also use the spectral function method to study modular constraints on CFT spectra, and discuss some implications of our results on CFTs of large
c
and large gap, in particular, to what extent the BTZ spectral density is universal.
Black hole/black ring transition Halder, Indranil; Lin, Ying-Hsuan
The journal of high energy physics,
01/2024, Letnik:
2024, Številka:
1
Journal Article
Recenzirano
Odprti dostop
A
bstract
We consider BPS states in M theory compactified on a Calabi-Yau threefold with one Kähler parameter, and investigate their relation to black holes and black rings. On the microscopic side, ...a characterization of the BPS degeneracy can be obtained from the non-perturbative part of the topological string free energy according to the Gopakumar-Vafa conjecture. On the macroscopic side, the Wald entropy of relevant black objects in the four-dimensional IIA description is computed from the perturbative part of the same topological string free energy following the work of Cardoso-de Wit-Mohaupt and then lifted to five-dimensional M theory through the Gaiotto-Strominger-Yin correspondence. For a given value of the M2 brane charge, we find that for small angular momenta, the microscopic BPS degeneracy matches the entropy of a rotating black hole, whereas an apparent transition occurs at a critical value of the angular momentum. Beyond this value, we find encouraging evidence that the microscopic counting is well approximated by the entropy of a black ring. We conclude by formulating a new puzzle involving the corrections due to degenerate worldsheet instantons.
A
bstract
We combine supersymmetric localization and the conformal bootstrap to study five-dimensional superconformal field theories. To begin, we classify the admissible counter-terms and derive a ...general relation between the five-sphere partition function and the conformal and flavor central charges. Along the way, we discover a new superconformal anomaly in five dimensions. We then propose a precise triple factorization formula for the five-sphere partition function, that incorporates instantons and is consistent with flavor symmetry enhancement. We numerically evaluate the central charges for the rank-one Seiberg and Morrison-Seiberg theories, and find strong evidence for their saturation of bootstrap bounds, thereby determining the spectra of long multiplets in these theories. Lastly, our results provide new evidence for the
F
-theorem and possibly a
C
-theorem in five-dimensional superconformal theories.
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