Related papers: A Multitrace Approach to Noncommutative \Phi_2^4
We study $\mathcal{N}=4$ supersymmetric QED in three dimensions, on a three-sphere, with 2N massive hypermultiplets and a Fayet-Iliopoulos parameter. We identify the exact partition function of the theory with a conical (Mehler) function.…
We study the phase diagram and critical behavior of the two-dimensional square-lattice fully frustrated XY model (FFXY) and of two related models, a lattice discretization of the Landau-Ginzburg-Wilson Hamiltonian for the critical modes of…
We consider a noncommutative field theory with space-time $\star$-commutators based on an angular noncommutativity, namely a solvable Lie algebra: the Euclidean in two dimension. The $\star$-product can be derived from a twist operator and…
The bispectral problem is motivated by an effort to understand and extend a remarkable phenomenon in Fourier analysis on the real line: the operator of time-and-band limiting is an integral operator admitting a second-order differential…
We show that an integrable four-dimensional non-unitary field theory that was recently proposed as a certain limit of the $\gamma_i$-deformed $\mathcal{N}=4$ SYM theory is incomplete and not conformal -- not even in the planar limit. We…
There are good reasons to suspect that spacetime at Planck scales is noncommutative. Typically this noncommutativity is controlled by fixed "vectors" or "tensors" with numerical entries. For the Moyal spacetime, it is the antisymmetric…
The Fock-space Hamiltonian truncation method is developed further, paying particular attention to the treatment of the scalar field zero mode. This is applied to the two-dimensional Phi^4 theory in the phase where the Z_2-symmetry is…
Let $E/F$ be an extension of number fields with $\mathrm{Gal}(E/F)$ simple and nonabelian. In [G] the first named author suggested an approach to nonsolvable base change and descent of automorphic representations of $\mathrm{GL}_2$ along…
We investigate quantum corrections in non-commutative gauge theory on fuzzy sphere. We study translation invariant models which classically favor a single fuzzy sphere with U(1) gauge group. We evaluate the effective actions up to the two…
We discuss gauge theories for commutative but non-associative algebras related to the $ SO(2k+1)$ covariant finite dimensional fuzzy $2k$-sphere algebras. A consequence of non-associativity is that gauge fields and gauge parameters have to…
Fermi arcs in Weyl semimetals provide a unique platform for surface-state engineering, yet di rectly tracking of their evolution under surface tuning remains experimentally challenging. Here we theoretically propose that nonreciprocal…
Renormalizable $\phi^{\star 4}_4$ models on Moyal space have been obtained by modifying the commutative propagator. But these models have a divergent "naive" commutative limit. We explain here how to obtain a coherent such commutative limit…
We explore some general consequences of a proper, full enforcement of the "twisted Poincare'" covariance of Chaichian et al. [14], Wess [50], Koch et al. [34], Oeckl [41] upon many-particle quantum mechanics and field quantization on a…
We propose a universal non-linear sigma model field theory for one dimensional frustrated ferromagnets, which applies in the vicinity of a "quantum Lifshitz point", at which the ferromagnetic state develops a spin wave instability. We…
The moduli-space metric in the static non-Abelian charge-two sector of the Moyal-deformed CP^1 sigma model in 1+2 dimensions is analyzed. After recalling the commutative results of Ward and Ruback and the zeta-regularized construction of…
This work prolongs, using an operator method, the investigations started in our recent paper J. Math. Phys. 51., 102108 on the spectrum and states of the harmonic oscillator on twisted Moyal plane, where rather a Moyal-star-algebraic…
A fuzzy geometry is a certain type of spectral triple whose Dirac operator crucially turns out to be a finite matrix. This notion was introduced in [J. Barrett, J. Math. Phys. 56, 082301 (2015)] and accommodates familiar fuzzy spaces like…
We construct spherical harmonics for fuzzy spheres of even and odd dimensions, generalizing the correspondence between finite matrix algebras and fuzzy two-spheres. The finite matrix algebras associated with the various fuzzy spheres have a…
Guided by idealized but soluble nonrenormalizable models, a nontraditional proposal for the quantization of covariant scalar field theories is advanced, which achieves a term-by-term, divergence-free perturbation analysis of interacting…
A world-volume model of non-critical 3-brane is quantized in a strong coupling phase where fluctuations of the conformal mode become dominant. This phase, called the conformal-mode dominant phase, is realized at the very high energy far…