Related papers: A note on S-dual basis in free fermion system
We present the Quantum Paldus Transform: an efficient quantum algorithm for block-diagonalising fermionic, spin-free Hamiltonians in the second quantisation. Our algorithm implements an isometry between the occupation number basis of a…
In the SM gauge symmetries and fermion content of neutrinos, charged leptons and quarks, we study the effective four-fermion operators of Einstein-Cartan type and their contributions to the Schwinger-Dyson equations of fermion self-energy…
Recently a duality between a family of \mathcal{N}=2 supersymmetric higher spin theories on AdS3, and the 't Hooft like limit of a class of Kazama-Suzuki models (that are parametrised by N and k) was proposed. The higher spin theories can…
We establish self-duality of super D3-brane theory as an exact symmetry of the action both in the Lagrangian and Hamiltonian formalism. In the Lagrangian formalism, the action is shown to satisfy the Gaillard-Zumino condition. This…
Behavior of doped fermions in $Z_2$ gauge theories for the quantum dimer and eight-vertex models is studied. Fermions carry charge and spin degrees of freedom. In the confinement phase of the $Z_2$ gauge theories, these internal symmetries…
We show that all fermions of one generation of the Standard Model (SM) can be elegantly described by a single fixed parity (say even) inhomogeneous real-valued differential form in seven dimensions. In this formalism the full kinetic term…
Spontaneous symmetry breaking is studied within a simple version of the light-front sigma model with fermions. Its vacuum structure is derived by an implementation of global symmetries in terms of unitary operators in a finite volume with…
In this paper we continue the development of quantum holonomy theory, which is a candidate for a fundamental theory based on gauge fields and non-commutative geometry. The theory is build around the QHD(M) algebra, which is generated by…
Two quantum theories which look different but are secretly describing the same low-energy physics are said to be dual to each other. When realized in the Topological Holography formalism, duality corresponds to changing the gapped boundary…
A Fourier transform S is defined for the quantum double D(G) of a finite group G. Acting on characters of D(G), S and the central ribbon element of D(G) generate a unitary matrix representation of the group SL(2,Z). The characters form a…
We show the complete integrability of N=2 nonstandard KP flows establishing the biHamiltonian structures. One of Hamiltonian structures is shown to be isomorphic to the nonlinear N=2 $\hat W_{\infty}$ algebra with the bosonic sector having…
We use the Kantor-Susskind\cite{kantsuss} model of fermions as "dumbbells" connecting points on a cubic lattice to points on its dual, to define a duality between local fermionic models invariant under a $Z_2$ gauge symmetry and models of…
Based on a nonabelian generalization of electric-magnetic duality, the Dualized Standard Model (DSM) suggests a natural explanation for exactly 3 generations of fermions as the `dual colour' $\widetilde{SU}(3)$ symmetry broken in a…
We examine various properties of double field theory and the doubled string sigma model in the context of geometric quantisation. In particular we look at T-duality as the symplectic transformation related to an alternative choice of…
Some quantum field theories described by non-Hermitian Hamiltonians are investigated. It is shown that for the case of a free fermion field theory with a $\gamma_5$ mass term the Hamiltonian is $\cal PT$-symmetric. Depending on the mass…
In this paper, we show that the Hamiltonian approach to loop quantum gravity has a fermion doubling problem. To obtain this result, we couple loop quantum gravity to a free massless scalar and a chiral fermion field, gauge fixing the many…
In one dimensional quantum gases there is a well known "duality" between hard core bosons and non-interacting fermions. However, at the field theory level, no exact duality connecting strongly interacting bosons to weakly interacting…
A recent derivation of the interpolation between the free energy and conformal anomaly for free fields on spheres is generalised to hemispheres with Neumann (N) and Dirichlet (D) conditions at the rim for GJMS scalar fields. It is shown…
We show that various holomorphic quantities in supersymmetric gauge theories can be conveniently computed by configurations of D4-branes and D6-branes. These D-branes intersect along a Riemann surface that is described by a holomorphic…
The concept of spin-base invariance is extended to arbitrary integer dimension $d \geq 2$. Explicit formulas for the spin connection as a function of the Dirac matrices are found. We disclose the hidden spin-base invariance of the vielbein…