Bernardo Zan
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View article: Analytic results in conformal field theory
Analytic results in conformal field theory Open
Since the 1980s, many exact results have been discovered in $2d$ CFT, from critical exponents to correlation functions to complete solutions of certain models. In $d>2$, there is a wealth of numerical results as well as promising analytic …
View article: Phases of 2d Gauge Theories and Symmetric Mass Generation
Phases of 2d Gauge Theories and Symmetric Mass Generation Open
We study the dynamics and phase structure of Abelian gauge theories in $d=1+1$ dimensions. These include $U(1)$ gauge theory coupled to a scalar and a fermion, as well as the two-flavour Schwinger model with different charges. Both theorie…
View article: Quantum Groups as Global Symmetries II. Coulomb Gas Construction
Quantum Groups as Global Symmetries II. Coulomb Gas Construction Open
We study a conformal field theory that arises in the infinite-volume limit of a spin chain with $U_q(sl_2)$ global symmetry. Most operators in the theory are defect-ending operators which allows $U_q(sl_2)$ symmetry transformations to act …
View article: Quantum Groups as Global Symmetries
Quantum Groups as Global Symmetries Open
We study quantum field theories which have quantum groups as global internal symmetries. We show that in such theories operators are generically non-local, and should be thought as living at the ends of topological lines. We describe the g…
View article: Phase Diagram of the Two-Flavor Schwinger Model at Zero Temperature
Phase Diagram of the Two-Flavor Schwinger Model at Zero Temperature Open
We examine the phase structure of the two-flavor Schwinger model as a function of the θ angle and the two masses, m1 and m2. In particular, we find interesting effects at θ=π: along the SU(2)-invariant line m1=m2=m, in the regime where m i…
View article: Phase Diagram of the Two-Flavor Schwinger Model at Zero Temperature
Phase Diagram of the Two-Flavor Schwinger Model at Zero Temperature Open
We examine the phase structure of the two-flavor Schwinger model as a function of the $θ$-angle and the two masses, $m_1$ and $m_2$. In particular, we find interesting effects at $θ=π$: along the $SU(2)$-invariant line $m_1 = m_2 = m$, in …
View article: Discrete chiral symmetry and mass shift in the lattice Hamiltonian approach to the Schwinger model
Discrete chiral symmetry and mass shift in the lattice Hamiltonian approach to the Schwinger model Open
We revisit the lattice formulation of the Schwinger model using the Kogut-Susskind Hamiltonian approach with staggered fermions. This model, introduced by Banks et al. Phys. Rev. D 13, 1043 (1976)10.1103/PhysRevD.13.1043, contains the mass…
View article: Discrete Chiral Symmetry and Mass Shift in Lattice Hamiltonian Approach to Schwinger Model
Discrete Chiral Symmetry and Mass Shift in Lattice Hamiltonian Approach to Schwinger Model Open
We revisit the lattice formulation of the Schwinger model using the Kogut-Susskind Hamiltonian approach with staggered fermions. This model, introduced by Banks et al., contains the mass term $m_{\rm lat} \sum_{n} (-1)^{n} χ^\dagger_n χ_n$…
View article: The $\mathcal{N} = 2$ Prepotential and the Sphere Free Energy
The $\mathcal{N} = 2$ Prepotential and the Sphere Free Energy Open
We study the mass-deformed sphere free energy of three-dimensional $\mathcal{N} = 2$ superconformal field theories with holographic duals. Building on previous observations, we conjecture a proportionality relation between the sphere free …
View article: A functional approach to the numerical conformal bootstrap
A functional approach to the numerical conformal bootstrap Open
A bstract We apply recently constructed functional bases to the numerical conformal bootstrap for 1D CFTs. We argue and show that numerical results in this basis converge much faster than the traditional derivative basis. In particular, tr…
View article: Studies in strongly coupled quantum field theories and renormalization group flows
Studies in strongly coupled quantum field theories and renormalization group flows Open
This thesis presents studies in strongly coupled Renormalization Group (RG) flows. In the first part, we analyze the subject of non-local Conformal Field Theories (CFTs), arising as continuous phase transitions of statistical models with l…
View article: Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$
Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$ Open
We study complex CFTs describing fixed points of the two-dimensional Q -state Potts model with Q≻ 4 . Their existence is closely related to the weak first-order phase transition and the "walking" renormalization group (RG) behavior …
View article: Report on 1808.04380v2
Report on 1808.04380v2 Open
We study complex CFTs describing fixed points of the two-dimensional Q-state Potts model with Q > 4. Their existence is closely related to the weak first-order phase transition and the "walking" renormalization group (RG) behavior present …
View article: A scaling theory for the long-range to short-range crossover and an infrared duality
A scaling theory for the long-range to short-range crossover and an infrared duality Open
We study the second-order phase transition in the d-dimensional Ising model with long-range interactions decreasing as a power of the distance $1/r^{d+s}$ . For s below some known value $s_*$ , the transition is described by a conformal fi…
View article: Long-Range Critical Exponents near the Short-Range Crossover
Long-Range Critical Exponents near the Short-Range Crossover Open
The d-dimensional long-range Ising model, defined by spin-spin interactions decaying with the distance as the power 1/r^{d+s}, admits a second-order phase transition with continuously varying critical exponents. At s=s_{*}, the phase trans…
View article: Non-gaussianity of the critical 3d Ising model
Non-gaussianity of the critical 3d Ising model Open
We discuss the 4pt function of the critical 3d Ising model, extracted from recent conformal bootstrap results. We focus on the non-gaussianity Q – the ratio of the 4pt function to its gaussian part given by three Wick contractions. This …
View article: Report on 1612.02436v2
Report on 1612.02436v2 Open
We discuss the 4pt function of the critical 3d Ising model, extracted from recent conformal bootstrap results.We focus on the non-gaussianity Q -the ratio of the 4pt function to its gaussian part given by three Wick contractions.This ratio…
View article: Report on 1612.02436v2
Report on 1612.02436v2 Open
We discuss the 4pt function of the critical 3d Ising model, extracted from recent conformal bootstrap results.We focus on the non-gaussianity Q -the ratio of the 4pt function to its gaussian part given by three Wick contractions.This ratio…