Related papers: The patching of critical points using quantum grou…
Deconfined quantum criticality describes continuous phase transitions that are not captured by the Landau-Ginzburg paradigm. Here, we investigate deconfined quantum critical points in the long-range, anisotropic Heisenberg chain. With…
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…
We present a procedure for averaging one-parameter random unitary groups and random self-adjoint groups. Central to this is a generalization of the notion of weak convergence of a sequence of measures and the corresponding generalization of…
We propose a method to determine the quantum phase boundaries of one-dimensional systems using sine-square deformation (SSD). Based on the proposition, supported by several exactly solved cases though not proven in full generality, that "if…
In conventional gauge theory, a charged point particle is described by a representation of the gauge group. If we propagate the particle along some path, the parallel transport of the gauge connection acts on this representation. The…
We revisit the problem of two dimensional metals in the vicinity of a quantum phase transition to incommensurate $\mathbf{Q}=2k_F$ charge density wave order, where the order parameter wave vector $\mathbf{Q}$ connects two hot spots on the…
In this review we describe a non-trivial relationship between perturbative gauge theory and gravity scattering amplitudes. At the semi-classical or tree level, the scattering amplitudes of gravity theories in flat space can be expressed as…
In the context of gauge-Yukawa theories with trans-Planckian asymptotic safety, quantum scale symmetry can prevent the appearance in the Lagrangian of couplings that would otherwise be allowed by the gauge symmetry. Such couplings…
Group theory is extremely successful in characterizing the symmetries in quantum systems, which greatly simplifies and unifies our treatments of quantum systems. Here we introduce the concept of the symmetry for a quantum Boltzmann machine…
We analyse a $2+1$ dimensional defect field theory on a two sphere in an external magnetic field. The theory is holographically dual to probe D5-branes in global AdS$_5\times S^5$ background. At any finite magnetic field only the confined…
In this review we study quantum field theories and conformal field theories with global symmetries in the limit of large charge for some of the generators of the symmetry group. At low energy the sectors of the theory with large charge are…
The measurement process is considered for quantum field theory on curved spacetimes. Measurements are carried out on one QFT, the "system", using another, the "probe" via a dynamical coupling of "system" and "probe" in a bounded spacetime…
The unitary S-matrix for the space-time non-commutative QED is constructed using the $\star$-time ordering which is needed in the presence of derivative interactions. Based on this S-matrix, perturbation theory is formulated and Feynman…
We establish the existence of fixed points for certain gauge theories candidate to be magnetic duals of QCD with one adjoint Weyl fermion. In the perturbative regime of the magnetic theory the existence of a very large number of fixed…
In the context of constrained quantum mechanics, reference systems are used to construct relational observables that are invariant under the action of the symmetry group. Upon measurement of a relational observable, the reference system…
These notes summarise a talk surveying the combinatorial or Hamiltonian quantisation of three dimensional gravity in the Chern-Simons formulation, with an emphasis on the role of quantum groups and on the way the various physical constants…
We study the QCD phase diagram, in particular we study the critical points of the two main QCD phase transitions, confinement and chiral symmetry breaking. Confinement drives chiral symmetry breaking, and, due to the finite quark mass, at…
Conformal field theory (CFT) is an extremely powerful tool for explicitly computing critical exponents and correlation functions of statistical mechanics systems at a second order phase transition, or of condensed matter systems at a…
Gauge theory underpins the quantum field theories of the standard model, and in a previous paper was shown via a geometric approach to describe classical electromagnetism in a form which approximates QED. Here we formalize and generalize…
We explore the fixed-point structure of QED-like theories upon the inclusion of a Pauli spin-field coupling. We concentrate on the fate of UV-stable fixed points recently discovered in $d=4$ spacetime dimensions upon generalizations to…