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Applied Conformal Field Theory
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These lectures consisted of an elementary introduction to conformal field theory, with some applications to statistical mechanical systems, and fewer to string theory. Contents: 1. Conformal theories in d dimensions 2. Conformal theories in 2 dimensions 3. The central charge and the Virasoro algebra 4. Kac determinant and unitarity 5. Identication of m = 3 with the critical Ising model 6. Free bosons and fermions 7. Free fermions on a torus 8. Free bosons on a torus 9. Affine Kac-Moody algebras and coset constructions 10. Advanced applications
Forward citations
Cited by 48 Pith papers
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The "not-A", RSPT and Potts phases in an $S_3$-invariant chain
A two-parameter S3-invariant spin chain has four gapped phases, including a new 'not-A' phase and a representation symmetry-protected topological phase, with all transitions in the three-state Potts universality class.
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An Effective String Theory Toolbox for Quantum Hall Interfaces II: Majorana Fermions on Fluctuating Moore-Read Worldsheets
On a fluctuating Moore-Read interface, the changing line element fixes a universal half-density transport law for the chiral Majorana mode, and the Majorana stress tensor mediates its coupling to the shape dynamics.
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Fixed-point tensor network for compactified boson conformal field theory
Fixed-point tensors built from open-string boundary data reproduce the closed-string spectrum of the compactified boson at generic radius and generate stable RG flows with a controllable marginal deformation.
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Monte Carlo reconstruction of symmetry-twisted partition function ratios: the critical 3D Ising
Monte Carlo reconstruction via interpolating family and flat histograms computes the Z2-twisted thermodynamic Casimir difference in the critical 3D Ising model as 0.327(2).
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Hydrodynamics of perfect fluids with anomalies from the fermionic path integral
The fermionic path integral in the infrared yields hydrodynamic actions for anomalous perfect fluids, including four- and five-dimensional transgression forms from anomaly inflow.
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Non-invertible Symmetries in Weyl Fermions, and Applications to Fermion-Boundary Scattering Problem
Constructs a family of non-invertible topological defects in n Weyl fermion theories via unfolding of G-symmetric boundary conditions for Dirac fermions, with explicit descriptions for U(1)^n and applications to fermi...
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Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries
Gapped phases dual to massless RG flows in 2D CFTs exhibit unusual ordering via spontaneous breaking of non-group-like symmetries and are characterized using smeared boundary CFTs applied to smeared Ishibashi states.
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Descending into the Modular Bootstrap
Numerical search finds candidate modular-invariant spectra with integer degeneracies for 1 < c < 8/7 and hints at a stronger gap bound near c = 1.
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Tensor renormalization group approach to critical phenomena via symmetry-twisted partition functions
Tensor renormalization group computes symmetry-twisted partition functions to identify critical points solely from them, yielding Tc=2.2017(2) and nu=0.663(33) for the 3D O(2) model plus TBKT=0.8928(2) for the 2D O(2)...
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Strong zero modes in integrable spin-S chains
Exact strong zero modes exist for integrable spin-S XXZ chains with open boundaries; for integer S they localize in a weak Hilbert-Schmidt sense, not as sharp edge operators.
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Revisiting Schr\"odinger CFTs: Factorization, Massless Particles, and a Path to the Bootstrap
Schrödinger CFTs are reformulated via a harmonic-trap thermofield double, giving a state-operator correspondence for all operators and a factorization proof of non-renormalization.
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Mind the crosscap: $\tau$-scaling in non-orientable gravity and time-reversal-invariant systems
Non-orientable topological gravity produces a resummed topological expansion whose late-time behavior matches the GOE universality class of random matrix theory for time-reversal invariant chaotic systems.
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A systematic search for conformal field theories in very small spaces
A symmetry-free entropy search on four-site states recovers known CFTs and yields unclassified candidate CFTs with 1<c<2.
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Non-Local Conserved Currents and Continuous Non-Invertible Symmetries
Non-local conserved currents attached to topological lines generate continuous non-invertible symmetries in 1+1d CFTs, with new examples in SU(2)_k WZW and minimal model products.
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Exploring nontrivial topology at quantum criticality in a superconducting processor
Experimental preparation of topologically nontrivial critical states of the cluster Ising model on a 100-qubit superconducting processor, verified by boundary g-function and two-fold entanglement spectrum degeneracy u...
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Coupled minimal models revisited II: Constraints from permutation symmetry
For coupled large-m minimal models with N=5,6,7, every permutation-charged current below spin 10 acquires an anomalous dimension, so the IR fixed points show no extended chiral algebra in that range.
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Topological Transition on the Conformal Manifold
Fermionic conformal field theories on a line of couplings can pair up so that opposite sides differ by an invertible topological order, a continuous topological transition that maps to Kramers-Wannier duality after bo...
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Bosonization versus the Nielsen-Ninomiya theorem
The 2D modified Villain model's Weyl operators reproduce free Dirac correlations in the continuum, and their no-doubler Dirac kernel is non-local, showing exactly how bosonization evades the Nielsen-Ninomiya theorem.
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$BMS_3$-like algebras via the $Z_N$-graded $u(1)^2$ Kac-Moody algebra
Compactification of the non-compact algebraic varieties of Z_N-graded Sugawara constructions on u(1)^2 Kac-Moody yields BMS3-like algebras Vir ⋊ F with F nilpotent of depth r < N for N>2, with depth tied to singularity order.
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Exponentiation of higher-point and higher-genus Virasoro conformal blocks in the semiclassical limit
Extends the exponentiation of Virasoro conformal blocks in the semiclassical limit to higher-point and higher-genus cases at the level of formal power series using an extended oscillator method.
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Double-Current Deformations of Two-Dimensional QFTs with Anomalies
Extends double-current deformations to anomalous 2D QFTs via dynamical gauge and Stueckelberg couplings, producing an anomaly-preserving holonomy integral kernel that Gaussian-transforms the compact boson partition function.
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Qubit discretizations of d=3 conformal field theories
A protocol extracts scaling dimensions of d=3 CFTs from the spectrum of qubit Hamiltonians on polyhedral lattices, achieving few-percent accuracy on the 3D Ising model with 20 qubits.
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Matrix-product operator dualities in integrable lattice models
MPO dualities with exact inverses transform the R-matrix into an extended R-matrix satisfying a modified Yang–Baxter algebra, while non-invertible dualities preserve the baxterization structure.
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Holographic Equidistribution
Equidistribution of Hecke operators in large N CFT limits reduces the partition function to light-state Poincaré series with an immediate interpretation as sums over handlebody geometries.
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Probing holographic conformal field theories
In a holographic CFT on a cylinder, a qutrit Unruh-DeWitt detector harvests more mana when the dual bulk scalar uses standard (Δ+) quantization than alternate (Δ−) quantization.
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Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
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Total instanton restriction via multiverse interference: Noncompact gauge theories and (-1)-form symmetries
Continuous-universe decomposition plus (-1)-form gauging eliminates every instanton in local QFTs, realized explicitly by switching 2D U(1) gauge theories to noncompact R gauge groups.
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Modular matrices of 2d Carrollian and warped CFTs
Explicit modular S and T matrices are derived for Carrollian (bms3) and warped CFT characters, with checks of S squared and unitarity.
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Modular evolutions and causality in two-dimensional conformal field theory
Modular flows preserve causal spacetime ordering inside causal diamonds, but a bilocal modular Hamiltonian can violate local commutativity at spacelike distances.
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Tomonaga-Luttinger Liquid Behavior in a Rydberg-encoded Spin Chain
A Rydberg-encoded spin chain shows power-law correlations, tunable Friedel oscillations, and linear light-cone dynamics consistent with Tomonaga-Luttinger liquid physics.
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Exotic phase transitions in spin ladders with discrete symmetries that emulate spin-1/2 bosons in two dimensions
A spin ladder emulating 2D spinful bosons is exactly mapped to a Z2 gauge theory of chargons and spinons, yielding solvable models for all phases and predictions of deconfined-type transitions.
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Quantum criticality and universality in stationary state of long-range Kitaev model
For critical-to-critical quenches in the long-range Kitaev chain, the stationary state shows the same effective central charge as the ground state, so universality can be read from the late-time state.
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Conformal Freeze-In from Neutrino Portal
A conformal freeze-in model with a neutrino portal can produce the observed dark matter abundance and, in part of its parameter space, the neutrino mass scale, while evading X-ray constraints for composite sterile-neu...
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Pre-Strings Lectures on Artificial Intelligence
Lecture notes define neural-network field theory and survey how it recovers known QFT/string results plus applied AI techniques for string problems.
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Organizing transitions and their cascades: Generalized symmetry enforcement in massless flows or Higgs transitions
The unbroken fusion ring symmetry FR(SU(2)_{p-2}) stabilizes the massless RG flow M(p,p+1)->M(p-1,p) by making every invariant IR primary field irrelevant.
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Extending fusion rules with finite subgroups: A general construction of $Z_{N}$ extended conformal field theories and their orbifoldings
Constructs Z_N extended fusion rings and modular partition functions for nonanomalous subgroups, extending to multicomponent systems and orbifoldings in CFTs.
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A Compact Story of Positivity in de Sitter
Compares two methods to resolve disagreements and prove positivity of anomalous dimensions for principal series fields coupled to compact scalar operators in de Sitter space.
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Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.
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Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
New classes of boundary and coupled conformal field theories are constructed from Z_N gauging, with a proposed dictionary to topological order, nonchiral anyons, and domain walls.
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Quantum entanglement entropy and Tomonaga-Luttinger liquid to liquid transition in biquadratic spin-1 XY chain with rhombic single-ion anisotropy
In a spin-1 XY chain with biquadratic coupling and rhombic anisotropy, numerical ground states reveal two c=1 Tomonaga-Luttinger liquid phases, three ferroquadrupolar nematic phases, and BKT-type transitions between them.
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Notes on noninvertible quantum symmetries in two dimensions
A procedure is given for computing partition functions of Rep(G) noninvertible symmetries on 2D nonabelian G orbifolds, with explicit verification that gauging recovers the original theory's partition function.
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Gauge Invariant and Generic Formulation of Magnetic Translations and so(3,1) Curtright-Zachos Generators
Gauge-invariant magnetic translation operators, built from a gauge-covariant pseudo-momentum P, reproduce Curtright-Zachos generators through a rotation-dilatation duality.
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Comments on Celestial CFT and $AdS_{3}$ String Theory
Extends H3+-WZNW celestial CFT to holographically generate MHV amplitudes in Klein space, deriving dictionary, stress tensor, correlators, OPE and PDEs from KZ equations.
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Lectures on Semiclassical Methods for Composite Operators
Lecture notes develop semiclassical methods to compute large-n scaling dimensions of composite operators in CFTs, recovering known results in free theory and deriving one-loop corrections at the Wilson-Fisher fixed point.
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Lecture notes on strings in AdS$_3$ from the worldsheet and the AdS$_3$/CFT$_2$ duality
Lecture notes deliver a self-contained pedagogical overview of worldsheet strings in AdS3 with NSNS flux, summarizing 25 years of results with emphasis on spectrally flowed correlation functions.
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Lectures on Naturalness, String Landscape and Multiverse
Lecture notes providing a technical introduction to naturalness problems and the string theory landscape for graduate students.
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Spectral Networks: Bridging higher-rank Teichm\"uller theory and BPS states
A comprehensive introduction to spectral networks that develops higher-rank Teichmüller theory in parallel with class S gauge theory and BPS spectra.
- Lecture notes on conformal field theory
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