Related papers: Wall-Crossing Effects on Quiver BPS Algebras
We study phase structures of quantum field theories in fuzzy geometries. Several examples of fuzzy geometries as well as QFT's on such geometries are considered. They are fuzzy spheres and beyond as well as noncommutative deformations of…
We consider Yang-Baxter equations arising from its associative analog and study corresponding exchange relations. They generate finite-dimensional quantum algebras which have form of coupled ${\rm GL}(N)$ Sklyanin elliptic algebras. Then we…
A classical solution to the Yang-Mills theory is given a new semiclassical interpretation. The boundary value problem on a complex time contour which arises from the semiclassical approximation to multiparticle scattering amplitudes is…
We prove sharp spectral transition in the arithmetics of phase between localization and singular continuous spectrum for Diophantine almost Mathieu operators. We also determine exact exponential asymptotics of eigenfunctions and of…
We prove that the Gieseker moduli space of stable sheaves on a smooth projective threefold $X$ of Picard rank 1 is separated from the moduli space of PT stable objects by a single wall in the space of Bridgeland stability conditions on $X$,…
Quasicrystals are metallic alloys that possess long-range, aperiodic structures with diffraction symmetries forbidden to conventional crystals. Since the discovery of quasicrystals by Schechtman et al. at 1984 (ref. 1), there has been…
Yang-Baxter type models are integrable deformations of integrable field theories, such as the principal chiral model on a Lie group $G$ or $\sigma$-models on (semi-)symmetric spaces $G/F$. The deformation has the effect of breaking the…
A class of above-barrier quantum-scattering problems is shown to provide an experimentally-accessible platform for studying $\mathcal{PT}$-symmetric Schr\"odinger equations that exhibit spontaneous $\mathcal{PT}$ symmetry breaking despite…
This is a review on infinite non-abelian symmetries in two-dimensional field theories. We show how any integrable QFT enjoys the existence of infinitely many {\bf conserved} charges. These charges {\bf do not commute} between them and…
Altermagnetism, a novel magnetic phase characterized by symmetry-protected, momentum-dependent spin splitting and collinear compensated magnetic moments, has thus far been explored primarily in periodic crystals. In this Letter, we extend…
D3 and D7-branes intersecting in 2+1 dimensions give rise at low energies to N=4 supersymmetric Yang-Mills theory coupled to defect fermions in the fundamental representation. This theory undergoes a BKT-type phase transition from a…
We provide a general framework for wall-crossing of equivariant K-theoretic enumerative invariants of appropriate moduli stacks $\mathfrak{M}$, by lifting Joyce's homological universal wall-crossing arXiv:2111.04694 to K-theory and to…
I briefly argue for logical necessity to incorporate, besides c, hbar, two fundamental length scales in the symmetries associated with the interface of gravitational and quantum realms. Next, in order to clear the proverbial bush, I discuss…
The notion of limit stability on Calabi-Yau 3-folds is introduced by the author to construct an approximation of Bridgeland-Douglas stability conditions at the large volume limit. It has also turned out that the wall-crossing phenomena of…
We demonstrate that the occurrence of symmetry breaking phase transitions together with the emergence of a local order parameter in classical statistical physics is a consequence of the geometrical structure of probability space. To this…
We study certain categories associated to symmetric quivers with potential, called quasi-BPS categories. We construct semiorthogonal decompositions of the categories of matrix factorizations for moduli stacks of representations of (framed…
We study the physics of quark deconfinement on domain walls in four-dimensional supersymmetric SU(N) Yang-Mills theory, compactified on a small circle with supersymmetric boundary conditions. We numerically examine the properties of BPS…
These notes are based on work done in collaboration with Frank Ferrari. We show how to determine the spectra of stable BPS states in $N=2$ supersymmetric $SU(2)$ Yang-Mills theories that are asymptotically free, i.e. without and with…
We study conformally invariant boundary conditions that break part of the bulk symmetries. A general theory is developped for those boundary conditions for which the preserved subalgebra is the fixed algebra under an abelian orbifold group.…
We investigate the connections between flavored quivers, dimer models, and BPS pyramids for generic toric Calabi-Yau threefolds from various perspectives. We introduce a purely field theoretic definition of both finite and infinite pyramids…