arXiv subjects

Gokce Basar

Publications and source records attributed to Gokce Basar.

At least 37 records · Page 2Linked to original sources

arXiv2018

Finite Density $QED_{1+1}$ Near Lefschetz Thimbles

One strategy for reducing the sign problem in finite-density field theories is to deform the path integral contour from real to complex fields. If the deformed manifold is the appropriate combination of Lefschetz thimbles -- or somewhat close to them -- the sign problem is alleviated. Gauge theories lack a well-defined thimble decomposition, and therefore it is unclear how to carry out a generalized thimble method. In this paper we discuss some of the conceptual issues involved by applying this method to $QED_{1+1}$ at finite density, showing that the generalized thimble method yields correct results with less computational effort than standard methods.

hep-lat↗

arXiv2017

Schwinger-Keldysh on the lattice: a faster algorithm and its application to field theory

A new algorithm is developed allowing the Monte Carlo study of a 1 + 1 dimensional theory in real time. The main algorithmic development is to avoid the explicit calculation of the Jacobian matrix and its determinant in the update process. This improvement has a wide applicability and reduces the cost of the update in thimble-inspired calculations from O(N^3) to less than O(N^2). As an additional feature, the algorithm leads to improved Monte Carlo proposals. We exemplify the use of the algorithm to the real time dynamics of a scalar ϕ^4 theory with weak and strong couplings.

hep-lat↗

arXiv2017

Interplay of Reggeon and photon in pA collisions

We discuss the effects of the electromagnetic interaction in high-energy proton collisions with nuclei of large Z at strong coupling $λ=g^2N_c$. Using the holographic dual limit of large $N_c>λ\gg 1$, we describe the Reggeon exchange as a twisted surface and show that it gets essentially modified by the electromagnetic interaction.

nucl-th↗

arXiv2017

Tempered transitions between thimbles

Quantum field theories with complex actions cannot be investigated using importance sampling due to the sign problem. One possible solution is to use the holomorphic gradient flow, a method we introduced related to the Lefschetz thimbles idea. In many cases the probability distribution generated by this method is multi-modal and standard Monte-Carlo sampling fails. We propose an algorithm that incorporates tempered proposals to solve this problem. We apply this algorithm to the 0+1 dimensional Thirring model at finite density for a parameter set where standard sampling fails and show that tempered proposals cure this problem.

hep-lat↗

arXiv2017

Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations

For a wide variety of quantum potentials, including the textbook `instanton' examples of the periodic cosine and symmetric double-well potentials, the perturbative data coming from fluctuations about the vacuum saddle encodes all non-perturbative data in all higher non-perturbative sectors. Here we unify these examples in geometric terms, arguing that the all-orders quantum action determines the all-orders quantum dual action for quantum spectral problems associated with a classical genus one elliptic curve. Furthermore, for a special class of genus one potentials this relation is particularly simple: this class includes the cubic oscillator, symmetric double-well, symmetric degenerate triple-well, and periodic cosine potential. These are related to the Chebyshev potentials, which are in turn related to certain ${\mathcal N}=2$ supersymmetric quantum field theories, to mirror maps for hypersurfaces in projective spaces, and also to topological $c=3$ Landau-Ginzburg models and `special geometry'. These systems inherit a natural modular structure corresponding to Ramanujan's theory of elliptic functions in alternative bases, which is especially important for the quantization. Insights from supersymmetric quantum field theory suggest similar structures for more complicated potentials, corresponding to higher genus. Our approach is very elementary, using basic classical geometry combined with all-orders WKB.

hep-th↗

arXiv2016

Monte Carlo calculations of the finite density Thirring model

We present results of the numerical simulation of the two-dimensional Thirring model at finite density and temperature. The severe sign problem is dealt with by deforming the domain of integration into complex field space. This is the first example where a fermionic sign problem is solved in a quantum field theory by using the holomorphic gradient flow approach, a generalization of the Lefschetz thimble method.

hep-lat↗

arXiv2016

Monte Carlo study of real time dynamics

Monte Carlo studies involving real time dynamics are severely restricted by the sign problem that emerges from highly oscillatory phase of the path integral. In this letter, we present a new method to compute real time quantities on the lattice using the Schwinger-Keldysh formalism via Monte Carlo simulations. The key idea is to deform the path integration domain to a complex manifold where the phase oscillations are mild and the sign problem is manageable. We use the previously introduced "contraction algorithm" to create a Markov chain on this alternative manifold. We substantiate our approach by analyzing the quantum mechanical anharmonic oscillator. Our results are in agreement with the exact ones obtained by diagonalization of the Hamiltonian. The method we introduce is generic and in principle applicable to quantum field theory albeit very slow. We discuss some possible improvements that should speed up the algorithm.

hep-lat↗

arXiv2016

A study of symmetry breaking in a relativistic Bose gas using the contraction algorithm

A relativistic Bose gas at finite density suffers from a sign problem that makes direct numerical simulations not feasible. One possible solution to the sign problem is to re-express the path integral in terms of Lefschetz thimbles. Using this approach we study the relativistic Bose gas both in the symmetric phase (low-density) and the spontaneously broken phase (high-density). In the high-density phase we break explicitly the symmetry and determine the dependence of the order parameter on the breaking. We study the relative contributions of the dominant and sub-dominant thimbles in this phase. We find that the sub-dominant thimble only contributes substantially when the explicit symmetry breaking is small, a regime that is dominated by finite volume effects. In the regime relevant for the thermodynamic limit, this contribution is negligible.

hep-lat↗

arXiv2016

Fast Estimator of jacobians in Monte Carlo Integration on Lefschetz Thimbles

A solution to the sign problem is the so-called "Lefschetz thimble approach" where the domain of integration for field variables in the path integral is deformed from the real axis to a sub-manifold in the complex space. For properly chosen sub-manifolds ("thimbles") the sign problem disappears or is drastically alleviated. The parametrization of the thimble by real coordinates require the calculation of a jacobian with a computational cost of order O(V^3), where V is proportional to the spacetime volume. In this note we propose two estimators for this jacobian with a computational cost of order O(V). We discuss analytically the regimes where we expect the estimator to work and show numerical examples in two different models.

hep-lat↗

arXiv2016

Sign problem and Monte Carlo calculations beyond Lefschetz thimbles

We point out that Monte Carlo simulations of theories with severe sign problems can be profitably performed over manifolds in complex space different from the one with fixed imaginary part of the action. We describe a family of such manifolds that interpolate between the tangent space at one critical point, where the sign problem is milder compared to the real plane but in some cases still severe, and the union of relevant thimbles, where the sign problem is mild but a multimodal distribution function complicates the Monte Carlo sampling. We exemplify this approach using a simple 0 + 1 dimensional fermion model previously used on sign problem studies and show that it can solve the model for some parameter values where a solution using Lefshetz thimbles was elusive.

hep-lat↗

arXiv2015

A Monte Carlo algorithm for simulating fermions on Lefschetz thimbles

A possible solution of the notorious sign problem preventing direct Monte Carlo calculations for systems with non-zero chemical potential is to deform the integration region in the complex plane to a Lefschetz thimble. We investigate this approach for a simple fermionic model. We introduce an easy to implement Monte Carlo algorithm to sample the dominant thimble. Our algorithm relies only on the integration of the gradient flow in the numerically stable direction, which gives it a distinct advantage over the other proposed algorithms. We demonstrate the stability and efficiency of the algorithm by applying it to an exactly solvable fermionic model and compare our results with the analytical ones. We report a very good agreement for a certain region in the parameter space where the dominant contribution comes from a single thimble, including a region where standard methods suffer from a severe sign problem. However, we find that there are also regions in the parameter space where the contribution from multiple thimbles is important, even in the continuum limit.

hep-lat↗

arXiv2015

Hydrodynamics, resurgence and trans-asymptotics

The second-order hydrodynamical description of a homogeneous conformal plasma that undergoes a boost- invariant expansion is given by a single nonlinear ordinary differential equation, whose resurgent asymptotic properties we study, developing further the recent work of Heller and Spalinski [Phys. Rev. Lett. 115, 072501 (2015)]. Resurgence clearly identifies the non-hydrodynamic modes that are exponentially suppressed at late times, analogous to the quasi-normal-modes in gravitational language, organizing these modes in terms of a trans-series expansion. These modes are analogs of instantons in semi-classical expansions, where the damping rate plays the role of the instanton action. We show that this system displays the generic features of resurgence, with explicit quantitative relations between the fluctuations about different orders of these non-hydrodynamic modes. The imaginary part of the trans-series parameter is identified with the Stokes constant, and the real part with the freedom associated with initial conditions.

hep-th↗

arXiv2015

A 4D-2D equivalence for large-N Yang-Mills theory

General string-theoretic considerations suggest that four-dimensional large-N gauge theories should have dual descriptions in terms of two-dimensional conformal field theories. However, for non-supersymmetric confining theories such as pure Yang-Mills theory, a long-standing challenge has been to explicitly show that such dual descriptions actually exist. In this paper, we consider the large-N limit of four-dimensional pure Yang-Mills theory compactified on a three-sphere in the solvable limit where the sphere radius is small compared to the strong length scale, and demonstrate that the confined-phase spectrum of this gauge theory coincides with the spectrum of an irrational two-dimensional conformal field theory.

hep-th↗

arXiv2015

Bose-Fermi Degeneracies in Large $N$ Adjoint QCD

We analyze the large $N$ limit of adjoint QCD, an $SU(N)$ gauge theory with $N_f$ flavors of massless adjoint Majorana fermions, compactified on $S^3 \times S^1$. We focus on the weakly-coupled confining small-$S^3$ regime. If the fermions are given periodic boundary conditions on $S^1$, we show that there are large cancellations between bosonic and fermionic contributions to the twisted partition function. These cancellations follow a pattern previously seen in the context of misaligned supersymmetry, and lead to the absence of Hagedorn instabilities for any $S^1$ size $L$, even though the bosonic and fermionic densities of states both have Hagedorn growth. Adjoint QCD stays in the confining phase for any $L \sim N^0$, explaining how it is able to enjoy large $N$ volume independence for any $L$. The large $N$ boson-fermion cancellations take place in a setting where adjoint QCD is manifestly non-supersymmetric at any finite $N$, and are consistent with the recent conjecture that adjoint QCD has emergent fermionic symmetries in the large $N$ limit.

hep-th↗

arXiv2015

Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems

The Nekrasov-Shatashvili limit for the low-energy behavior of N=2 and N=2* supersymmetric SU(2) gauge theories is encoded in the spectrum of the Mathieu and Lam'e equations, respectively. This correspondence is usually expressed via an all-orders Bohr-Sommerfeld relation, but this neglects non-perturbative effects, the nature of which is very different in the electric, magnetic and dyonic regions. In the gauge theory dyonic region the spectral expansions are divergent, and indeed are not Borel-summable, so they are more properly described by resurgent trans-series in which perturbative and non-perturbative effects are deeply entwined. In the gauge theory electric region the spectral expansions are convergent, but nevertheless there are non-perturbative effects due to poles in the expansion coefficients, and which we associate with worldline instantons. This provides a concrete analog of a phenomenon found recently by Drukker, Marino and Putrov in the large N expansion of the ABJM matrix model, in which non-perturbative effects are related to complex space-time instantons. In this paper we study how these very different regimes arise from an exact WKB analysis, and join smoothly through the magnetic region. This approach also leads to a simple proof of a resurgence relation found recently by Dunne and Unsal, showing that for these spectral systems all non-perturbative effects are subtly encoded in perturbation theory, and identifies this with the Picard-Fuchs equation for the quantized elliptic curve.

hep-th↗

arXiv2014

Casimir energy of confining large $N$ gauge theories

Four-dimensional asymptotically-free large $N$ gauge theories compactified on $S^3_R \times \mathbb{R}$ have a weakly-coupled confining regime when $R$ is small compared to the strong scale. We compute the vacuum energy of a variety of confining large $N$ non-supersymmetric gauge theories in this calculable regime, where the vacuum energy can be thought of as the $S^3$ Casimir energy. The $N=\infty$ renormalized vacuum energy turns out to vanish in all of the large $N$ gauge theories we have examined, confirming a striking prediction of temperature-reflection symmetry.

hep-th↗

arXiv2014

A scaling relation between proton-nucleus and nucleus-nucleus collisions

It is recently discovered that at high multiplicy, the proton-nucleus ($pA$) collisions give rise to two particle correlations that are strikingly similar to those of nucleus-nucleus ($AA$) collisions at the same multiplicity, although the system size is smaller in $pA$. Using an independent cluster model and a simple conformal scaling argument, where the ratio of the mean free path to the system size stays constant at fixed multiplicity, we argue that flow in $pA$ emerges as a collective response to the fluctuations in the position of clusters, just like in $AA$ collisions. With several physically motivated and parameter free rescalings of the recent LHC data, we show that this simple model captures the essential physics of elliptic and triangular flow in $pA$ collisions.

hep-ph↗

arXiv2014

A scaling relation between pA and AA collisions

We compare the flow-like correlations in high multiplicity proton-nucleus ($p+A$) and nucleus-nucleus ($A+A$) collisions. At fixed multiplicity, the correlations in these two colliding systems are strikingly similar, although the system size is smaller in $p+A$. Based on an independent cluster model and a simple conformal scaling argument, where the ratio of the mean free path to the system size stays constant at fixed multiplicity, we argue that flow in $p+A$ emerges as a collective response to the fluctuations in the position of clusters, just like in $A+A$ collisions. With several physically motivated and parameter free rescalings of the recent LHC data, we show that this simple model captures the essential physics of elliptic and triangular flow in $p+A$ collisions. We also explore the implications of the model for jet energy loss in $p+A$, and predict slightly larger transverse momentum broadening in $p+A$ than in $A+A$ at the same multiplicity.

nucl-th↗