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Inspired by the structural unification of unitary groups (quantum field theory) with orthogonal groups (relativity) proposed recently through a non-division algebra, we construct a hypercomplex field theory with an internal symmetry that…
Two-dimensional conformal field theory (CFT) has several sources: the search for simple examples of quantum field theory, the description of surface critical phenomena, the study of (super)string vacua. In the present overview of the…
We study one and two point functions of conformal field theories on spaces of maximal symmetry with and without boundaries and investigate their spectral representations. Integral transforms are found, relating the spectral decomposition to…
Quantum theory of 2d gravity for $c>1$ is examined as a non-critical string theory by taking account of the loop-correction of open strings whose end points are on the 2d world surface of the closed string. This loop-correction leads to a…
Constructing a holographic string theory dual for a CFT in the perturbative, weakly coupled regime is a holy grail for gauge/string dualities that would not only open the door for proofs of the AdS/CFT correspondence but could also provide…
Sen's action for chiral bosons in 2 dimensions describes two chiral scalars, one of which couples to the physical metric and one of which couples to a flat metric. It has a generalisation in which the flat metric is replaced by an arbitrary…
I point out that standard two dimensional, asymptotically free, non-linear sigma models, supplemented with terms giving a mass to the would-be Goldstone bosons, share many properties with four dimensional supersymmetric gauge theories, and…
We show that abelian bosonization of 1+1 dimensional fermion systems can be interpreted as duality transformation and, as a conseguence, it can be generalized to arbitrary dimensions in terms of gauge forms of rank $d-1$, where $d$ is the…
A supersymmetric approach to string quantum cosmology based on the non-compact, global duality symmetries of the effective action is developed. An N=2 supersymmetric action is derived whose bosonic component is the…
We consider $3$-dimensional conformal field theories with $U(N)_{\kappa}$ Chern Simons gauge fields coupled to bosonic and fermionic matter fields transforming in the fundamental representation of the gauge group. In these CFTs, we compute…
We consider a version of the $AdS_{d+1}/CFT_{d}$ correspondence, in which the bulk space is taken to be the quotient manifold $AdS_{d+1} /\Gamma$ with a fairly generic discrete group $\Gamma$ acting isometrically on $AdS_{d+1}$. We address…
Conformal field theory (CFT) has been extremely successful in describing large-scale universal effects in one-dimensional (1D) systems at quantum critical points. Unfortunately, its applicability in condensed matter physics has been limited…
We study conformal field theories (CFTs) and their classifications from a modern perspective based on the abstract algebraic formalism of symmetries or conserved charges, known as symmetry topological field theories (SymTFTs). By studying…
We provide a unified treatment of conformally soft Goldstone modes which arise when spin-one or spin-two conformal primary wavefunctions become pure gauge for certain integer values of the conformal dimension $\Delta$. This effort lands us…
We define a normalizable measure on the space of two-dimensional conformal field theories, which we interpret as a maximum ignorance ensemble. We test whether pure quantum gravity in AdS$_3$ is dual to the average over this ensemble. We…
Supersymmetric conformal field theories (SCFTs) form a unique subset of quantum field theories which provide powerful insights into strongly coupled critical phenomena. Here, we present a microscopic and non-perturbative realization of the…
We discuss two-dimensional conformal field theories (CFTs) which are invariant under gauging a non-invertible global symmetry. At every point on the orbifold branch of $c=1$ CFTs, it is known that the theory is self-dual under gauging a…
We study the cosmic microwave background (CMB) radiation in the unified description of the effective field theory (EFT) of dark energy that accommodates both scalar-tensor and vector-tensor theories. The boundaries of different classes of…
We study 2d $SU(N)$ QCD with an adjoint Dirac fermion. Assuming that the IR limit of the massless theory is captured by a WZW coset CFT, we show that this CFT can be decomposed into a sum of distinct CFTs, each representing a superselection…
The underlying reasons for the difficulty of unitarily implementing the whole conformal group $SO(4,2)$ in a massless Quantum Field Theory (QFT) are investigated in this paper. Firstly, we demonstrate that the singular action of the…