Markov Chain Monte Carlo Methods in Quantum Field Theories

Joseph, Anosh

doi:10.1007/978-3-030-46044-0

Cited by 14 publications

(11 citation statements)

References 29 publications

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“…which is thus consistent with the analytic estimate (6.1). 15 For other papers using MC methods in matrix models see, e.g., [36][37][38][39][40][41] and section 6.5 of [42]. In the explored region of parameter space the Metropolis-Hastings algorithm turned out to be faster than the Hybrid Monte Carlo one, taking into account autocorrelation.…”

Section: Orbifold Theorymentioning

confidence: 99%

1/N expansion of circular Wilson loop in $$ \mathcal{N} $$ = 2 superconformal SU(N) × SU(N) quiver

Beccaria

Tseytlin

2021

J. High Energ. Phys.

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Localization approach to $$ \mathcal{N} $$ N = 2 superconformal SU(N) × SU(N) quiver theory leads to a non-Gaussian two-matrix model representation for the expectation value of BPS circular SU(N) Wilson loop $$ \left\langle \mathcal{W}\right\rangle $$ W . We study the subleading 1/N2 term in the large N expansion of $$ \left\langle \mathcal{W}\right\rangle $$ W at weak and strong coupling. We concentrate on the case of the symmetric quiver with equal gauge couplings which is equivalent to the ℤ2 orbifold of the SU(2N) $$ \mathcal{N} $$ N = 4 SYM theory. This orbifold gauge theory should be dual to type IIB superstring in AdS5 × (S5/ℤ2). We present a string theory argument suggesting that the 1/N2 term in $$ \left\langle \mathcal{W}\right\rangle $$ W in the orbifold theory should have the same strong-coupling asymptotics λ3/2 as in the $$ \mathcal{N} $$ N = 4 SYM case. We support this prediction on the gauge theory side by a numerical study of the localization matrix model. We also find a relation between the 1/N2 term in the Wilson loop expectation value and the derivative of the free energy of the orbifold gauge theory on 4-sphere.

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Section: Orbifold Theorymentioning

confidence: 99%

1/N expansion of circular Wilson loop in $$ \mathcal{N} $$ = 2 superconformal SU(N) × SU(N) quiver

Beccaria

Tseytlin

2021

J. High Energ. Phys.

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“…15 For other papers using MC methods in matrix models see, e.g., [36,37,38,39,40,41] and section 6.5 of [42]. In the explored region of parameter space the Metropolis-Hastings algorithm turned out to be faster than the Hybrid Monte Carlo one, taking into account autocorrelation.…”

Section: Orbifold Theorymentioning

confidence: 99%

$1/N$ expansion of circular Wilson loop in $\mathcal N=2$ superconformal $SU(N)\times SU(N)$ quiver

Beccaria,

Tseytlin

2021

Preprint

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Localization approach to N " 2 superconformal SU pN q ˆSU pN q quiver theory leads to a non-Gaussian two-matrix model representation for the expectation value of BPS circular SU pN q Wilson loop xWy. We study the subleading 1{N 2 term in the large N expansion of xWy at weak and strong coupling. We concentrate on the case of the symmetric quiver with equal gauge couplings which is equivalent to the Z 2 orbifold of the SU p2N q N " 4 SYM theory. This orbifold gauge theory should be dual to type IIB superstring in AdS 5 ˆpS 5 {Z 2 q. We present a string theory argument suggesting that the 1{N 2 term in xWy in the orbifold theory should have the same strong-coupling asymptotics λ 3{2 as in the N " 4 SYM case. We support this prediction on the gauge theory side by a numerical study of the localization matrix model. We also find a relation between the 1{N 2 term in the Wilson loop expectation value and the derivative of the free energy of the orbifold gauge theory on 4-sphere.

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“…For a detailed review about HMC and its extension to rational HMC which is required for fermions, the interested readers can consult Ref. [25,26]. The two basic parts of HMC are, a) Use of integrator to evolve and propose a new configuration, b) accept or reject the proposed configuration.…”

Section: Basics Of Monte Carlo Methodsmentioning

confidence: 99%

Introduction to Monte Carlo for Matrix Models

Jha

2021

Preprint

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We consider a wide range of matrix models and study them using the Monte Carlo technique in the large N limit. The results we obtain agree with exact analytic expressions and recent numerical bootstrap methods for models with one and two matrices. We then present new results for several unsolved multi-matrix models where no other tool is yet available. In order to encourage an exchange of ideas between different numerical approaches to matrix models, we provide programs in Python that can be easily modified to study potentials other than the ones discussed. These programs were tested on a laptop and took between a few minutes to several hours to finish depending on the model, N , and the required precision.

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Markov Chain Monte Carlo Methods in Quantum Field Theories

Cited by 14 publications

References 29 publications

1/N expansion of circular Wilson loop in $$ \mathcal{N} $$ = 2 superconformal SU(N) × SU(N) quiver

1/N expansion of circular Wilson loop in $$ \mathcal{N} $$ = 2 superconformal SU(N) × SU(N) quiver

$1/N$ expansion of circular Wilson loop in $\mathcal N=2$ superconformal $SU(N)\times SU(N)$ quiver

Introduction to Monte Carlo for Matrix Models

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