Related papers: Direct Monte Carlo Computation of the 't~Hooft Par…
These notes have two parts. The first is a study of Nekrasov's deformed partition functions $Z(\ve_1,\ve_2,\vec{a};\q,\vec{\tau})$ of N=2 SUSY Yang-Mills theories, which are generating functions of the integration in the equivariant…
In this paper we shall investigate the possibility of solving U(1) theories on the non-commutative (NC) plane for arbitrary values of $\theta$ by exploiting Morita equivalence. This duality maps the NC U(1) on the two-torus with a rational…
We propose a new method to calculate expectation values of a delta function of the Hamiltonian, < \Psi \mid \delta(\hat{H} - E)\mid \Psi >. Since the delta function can be replaced with a Gaussian function, we evaluate < \Psi \mid…
The Quantum Monte Carlo method for spin 1/2 fermions at finite temperature is formulated for dilute systems with an s-wave interaction. The motivation and the formalism are discussed along with descriptions of the algorithm and various…
We propose a splitting Hamiltonian Monte Carlo (SHMC) algorithm, which can be computationally efficient when combined with the random mini-batch strategy. By splitting the potential energy into numerically nonstiff and stiff parts, one…
We compute by supersymmetric localization the expectation values of half-BPS 't Hooft line operators in $\mathcal{N}=2$ $U(N)$, $SO(N)$ and $USp(N)$ gauge theories on $S^1 \times \mathbb{R}^3$ with an $\Omega$-deformation. We evaluate the…
Using the BF version of pure Yang-Mills, it is possible to find a covariant representation of the 't Hooft magnetic flux operator. In this framework, 't Hooft's pioneering work on confinement finds an explicit realization in the continuum.…
We obtain the correct all-loop beta-function of pure N=1 super Yang-Mills theory from the supergravity solution of the warped deformed conifold, including also some nonperturbative corrections. The crucial ingredient is the gauge-gravity…
We consider $(3+1)$-dimensional $SU(N)/\mathbb Z_N$ Yang-Mills theory on a space-time with a compact spatial direction, and prove the following result: Under a continuous increase of the theta angle $\theta\to\theta+2\pi$, a 't Hooft…
Over the last several years, a new generation of quantum simulations has greatly expanded our understanding of charge density wave phase transitions in Hamiltonians with coupling between local phonon modes and the on-site charge density. A…
We test the AdS/CFT correspondence by computing the partition function of some $\mathcal{N}=2$ quiver Chern-Simons-matter theories on three-sphere. The M-theory backgrounds are of the Freund-Rubin type with the seven-dimensional internal…
Exact results in supersymmetric Chern-Simons and N=2 Yang-Mills theories can be used to examine the quantum behavior of observables and the structure of the perturbative series. For the U(2) x U(2) ABJM model, we determine the asymptotic…
We consider spaces of trial wavefunctions for ground states and edge excitations in the fractional quantum Hall effect that can be obtained in various ways. In one way, functions are obtained by analyzing the entanglement of the ground…
The hybrid Monte Carlo (HMC) algorithm is a ubiquitous method in computational physics with applications ranging from condensed matter to lattice QCD and beyond. However, HMC simulations often suffer from long autocorrelation times,…
We consider a variational approach to the finite temperature Yang-Mills theory in the Coulomb gauge. The partition function is computed in the ensemble of glueballs and quasi-gluons which emerge as eigenstates of the Coulomb gauge…
The time-dependent Hartree-Fock (TDHF) method is an approach to simulate the mean field dynamics of electrons within the assumption that the electrons move independently in their self-consistent average field and within the space of single…
We consider a class of quantum field theories and quantum mechanics, which we couple to $\mathbb Z_N$ topological QFTs, in order to classify non-perturbative effects in the original theory. The $\mathbb Z_N$ TQFT structure arises naturally…
We apply localization techniques to compute the partition function of a two-dimensional N=(2,2) R-symmetric theory of vector and chiral multiplets on S^2. The path integral reduces to a sum over topological sectors of a matrix integral over…
We define the quadratic algebra su(2)_{\alpha} which is a one-parameter deformation of the Lie algebra su(2) extended by a parity operator. The odd-dimensional representations of su(2) (with representation label j, a positive integer) can…
Suzuki-Trotter decomposition is a well-known technique used to calculate the partition function of quantum spin systems, in which the imaginary-time dependence of the partition function occurs inevitably. Since it is very difficult to…