Related papers: Modular Constraints on Conformal Field Theories wi…
Using the method of modular-invariant differential equations, we classify a family of Rational Conformal Field Theories with two and three characters having no Kac-Moody algebra. In addition to unitary and non-unitary minimal models, we…
We explore higher-dimensional conformal field theories (CFTs) in the presence of a conformal defect that itself hosts another sub-dimensional defect. We refer to this new kind of conformal defect as the composite defect. We elaborate on the…
We study conformal twist field four-point functions on a $\mathbb Z_N$ orbifold. We examine in detail the case $N=3$ and analyze theories obtained by replicated $N$-times a minimal model with central charge $c<1$. A fastly convergent…
We study the free energy of four-dimensional CFTs on deformed spheres. For generic nonsupersymmetric CFTs only the coefficient of the logarithmic divergence in the free energy is physical, which is an extremum for the round sphere. We then…
In this thesis we analyse three aspects of Conformal Field Theories (CFTs). First, we consider correlation functions of descendant states in two-dimensional CFTs. We discuss a recursive formula to calculate them and provide a computer…
We studied the marginal deformation of the $c=0$ topological conformal field theories (TCFT). We showed that topological $SL(2)$ Wess-Zumino-Witten (WZW) model, topological superconformal ghost system, TCFT constructed from the $N=2$…
We study the geometric action of some modular conjugations in two dimensional (2D) conformal field theories. We investigate the bipartition given by an interval when the system is in the ground state, either on the line or on the circle,…
We study analytically the constraints of the conformal bootstrap on the low-lying spectrum of operators in field theories with global conformal symmetry in one and two spacetime dimensions. We introduce a new class of linear functionals…
The method of large spin perturbation theory allows to analyse conformal field theories (CFT) by turning the crossing equations into an algebraic problem. We apply this method to a generic CFT with weakly broken higher spin (HS) symmetry,…
We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational,…
The trace anomaly of conformal field theories in four dimensions is characterized by '$a$' and '$c$'-functions. The scaling properties of the effective action of a CFT in the presence of boundaries is shown to be determined by $a$, $c$ and…
In this note we explore the application of modular invariance in 2-dimensional CFT to derive universal bounds for quantities describing certain state degeneracies, such as the thermodynamic entropy, or the number of marginal operators. We…
We study the holographic duality between the free $O(N)$ vector model and higher spin gravity. Conserved spinning primary currents of the conformal field theory (CFT) are dual to spinning gauge fields in the gravity. Reducing to independent…
Using the numerical modular bootstrap, we constrain the space of 1+1d CFTs with a finite non-invertible global symmetry described by a fusion category $\mathcal{C}$. We derive universal and rigorous upper bounds on the lightest…
We study two-dimensional conformal field theories (CFTs) with boundaries via the conformal bootstrap. We derive a positive semi-definite program from crossing symmetry of three observables: the annulus partition function, the two-point…
The holographic duals of higher spin theories on AdS_3 are described by the large N limit of a family of minimal model CFTs, whose symmetry algebra is equivalent to W(infinity)[lambda]. We study perturbations of these limit theories, and…
We argue that the existence of a modular differential equation implies that a certain vector vanishes in Zhu's C2 quotient space, and we check this assertion in numerous examples. If this connection is true in general, it would imply that…
We study the Virasoro conformal block decomposition of the genus two partition function of a two-dimensional CFT by expanding around a Z3-invariant Riemann surface that is a three-fold cover of the Riemann sphere branched at four points,…
The problem of finding boundary states in CFT, often rephrased in terms of "NIMreps" of the fusion algebra, has a natural extension to CFT on non-orientable surfaces. This provides extra information that turns out to be quite useful to give…
We consider a 2-dimensional conformal field theory (CFT) obtained from twisted compactification of the 4-dimensional N=4 super Yang-Mills theory on a Riemann surface with boundary. We find the boundary conditions to preserve some of the…