Modular invariance
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Modular A4 invariance and neutrino mixing Open
A bstract We study the phenomenological implications of the modular symmetry Γ(3) ≃ A 4 of lepton flavors facing recent experimental data of neutrino oscillations. The mass matrices of neutrinos and charged leptons are essentially given by…
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Fermionic modular categories and the 16-fold way Open
We study spin and super-modular categories systematically as inspired by fermionic topological phases of matter, which are always fermion parity enriched and modelled by spin topological quantum field theories at low energy. We formulate a…
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The gravity duals of modular Hamiltonians Open
In this work, we investigate modular Hamiltonians defined with respect to arbitrary spatial regions in quantum field theory states which have semi-classical gravity duals. We find prescriptions in the gravity dual for calculating the actio…
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Light-cone modular bootstrap and pure gravity Open
We explore the large spin spectrum in two-dimensional conformal field theories with a finite twist gap, using the modular bootstrap in the light-cone limit. By recursively solving the modular crossing equations associated with different PS…
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Modular flavor symmetry on a magnetized torus Open
We study the modular invariance in magnetized torus models. Modular invariant\nflavor model is a recently proposed hypothesis for solving the flavor puzzle,\nwhere the flavor symmetry originates from modular invariance. In this framework\n…
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The Weak Gravity Conjecture in three dimensions Open
We study weakly coupled U(1) theories in AdS3, their associated charged BTZ solutions, and their charged spectra. We find that modular invariance of the holographic dual two-dimensional CFT and compactness of the gauge group together imply…
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Eigenstate thermalization hypothesis and modular invariance of two-dimensional conformal field theories Open
We study properties of heavy-light-heavy three-point functions in\ntwo-dimensional CFTs by using the modular invariance of two-point functions on\na torus. We show that our result is non-trivially consistent with the condition\nof ETH (Eig…
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Generalised CP symmetry in modular-invariant models of flavour Open
The formalism of combined finite modular and generalised CP (gCP) sym-metries for theories of flavour is developed. The corresponding consistency conditions for the two symmetry transformations acting on the modulus τ and on the matter fie…
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Hierarchy of modular graph identities Open
The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities betwee…
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Quantum spaces are modular Open
At present, our notion of space is a classical concept. Taking the point of\nview that quantum theory is more fundamental than classical physics, and that\nspace should be given a purely quantum definition, we revisit the notion of\nEuclid…
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Modular symmetry anomaly in magnetic flux compactification Open
We study modular symmetry anomalies in four-dimensional low-energy effective\nfield theory, which is derived from six-dimensional supersymmetric $U(N)$\nYang-Mills theory by magnetic flux compactification. The gauge symmetry $U(N)$\nis bro…
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On invariants of Modular categories beyond modular data Open
We study novel invariants of modular categories that are beyond the modular data, with an eye towards a simple set of complete invariants for modular categories. Our focus is on the $W$-matrix--the quantum invariant of a colored framed Whi…
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High energy modular bootstrap, global symmetries and defects Open
We derive Cardy-like formulas for the growth of operators in different sectors of unitary 2 dimensional CFT in the presence of topological defect lines by putting an upper and lower bound on the number of states with scaling dimension in t…
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Modular invariance and the QCD angle Open
A bstract String compactifications on an orbi-folded torus with complex structure give rise to chiral fermions, spontaneously broken CP, modular invariance. We show that this allows simple effective theories of flavour and CP where: i) the…
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A Note on Modular Invariant Species Scale and Potentials Open
The species scale provides an upper bound for the ultraviolet cutoff of effective theories of gravity coupled to a number of light particle species. Modular invariant (super‐)potentials provide a simple and computable expression of the spe…
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Bootstrapping holographic warped CFTs or: how I learned to stop worrying and tolerate negative norms Open
A bstract We use modular invariance to derive constraints on the spectrum of warped conformal field theories (WCFTs) — nonrelativistic quantum field theories described by a chiral Virasoro and U(1) Kac-Moody algebra. We focus on holographi…
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Are neutrino masses modular forms? Open
We explore a new class of supersymmetric models for lepton masses and mixing angles where the role of flavour symmetry is played by modular invariance. The building blocks are modular forms of level N and matter supermultiplets, both trans…
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Weak Gravity Conjecture, Black Hole Entropy, and Modular Invariance Open
In recent literature, it has been argued that a mild form of the Weak Gravity Conjecture (WGC) is satisfied by wide classes of effective field theories in which higher-derivative corrections can be shown to shift the charge-to-mass ratios …
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Nonlocal gravity with worldline inversion symmetry Open
We construct a quadratic curvature theory of gravity whose graviton propagator around the Minkowski background respects wordline inversion symmetry, the particle approximation to modular invariance in string theory. This symmetry automatic…
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Reflections on conformal spectra Open
Here, we use modular invariance and crossing symmetry of conformal field theory to reveal approximate reflection symmetries in the spectral decompositions of the partition function in two dimensions in the limit of large central charge and…
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A minimal modular invariant neutrino model Open
A bstract We present a neutrino mass model based on modular symmetry with the fewest input parameters to date, which successfully accounts for the 12 lepton masses and mixing parameters through 6 real free parameters including the modulus.…
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Loop models, modular invariance, and three-dimensional bosonization Open
We consider a family of quantum loop models in 2+1 spacetime dimensions with\nmarginally long-ranged and statistical interactions mediated by a U$(1)$ gauge\nfield, both purely in 2+1 dimensions and on a surface in a 3+1 dimensional bulk\n…
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Modular Commutators in Conformal Field Theory Open
The modular commutator is a recently discovered entanglement quantity that quantifies the chirality of the underlying many-body quantum state. In this Letter, we derive a universal expression for the modular commutator in conformal field t…
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On the species scale, modular invariance and the gravitational EFT expansion Open
A bstract The concept of the species scale as the quantum gravity cut-off has been recently emphasised in the context of the Swampland program. Along these lines, we continue the quest for a precise understanding of its role within effecti…
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Classical codes and chiral CFTs at higher genus Open
A bstract Higher genus modular invariance of two-dimensional conformal field theories (CFTs) is a largely unexplored area. In this paper, we derive explicit expressions for the higher genus partition functions of a specific class of CFTs: …
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Black holes and higher depth mock modular forms Open
By enforcing invariance under S-duality in type IIB string theory compactified on a Calabi–Yau threefold, we derive modular properties of the generating function of BPS degeneracies of D4–D2–D0 black holes in type IIA string theory compact…
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Galois symmetry induced by Hecke relations in rational conformal field theory and associated modular tensor categories Open
Hecke operators relate characters of rational conformal field theories\n(RCFTs) with different central charges, and extend the previously studied\nGalois symmetry of modular representations and fusion algebras. We show that\nthe conductor …
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Fake Z Open
A bstract Recently introduced connections between quantum codes and Narain CFTs provide a simple ansatz to express a modular-invariant function $$ Z\left(\tau, \overline{\tau}\right) $$ in terms of a multivariate polynomial satisfyi…
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Modular flavor symmetry and vector-valued modular forms Open
A bstract We revisit the modular flavor symmetry from a more general perspective. The scalar modular forms of principal congruence subgroups are extended to the vector-valued modular forms, then we have more possible finite modular groups …
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Anomalies, extensions, and orbifolds Open
We investigate gauge anomalies in the context of orbifold conformal field theories. Such anomalies manifest as failures of modular invariance in the constituents of the orbifold partition function. We review how this irregularity is classi…