On the sign problem in 2D lattice super Yang-Mills

Catterall, Simon; Galvez, Richard; Joseph, Anosh; Mehta, Dhagash

doi:10.1007/jhep01(2012)108

Cited by 40 publications

(49 citation statements)

References 52 publications

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“…Next, consider the 16-supercharge model in two space-time dimensions. Even though this system admits a complex pfaffian as in four dimensions, extensive numerical evidence indicates that there is no sign problem even at non-zero lattice spacing (and certainly in the continuum limit) [33][34][35][36].…”

Section: The Phase Of the Pfaffianmentioning

confidence: 99%

N=4supersymmetry on a space-time lattice

Catterall¹,

Schaich²,

Damgaard³

et al. 2014

Phys. Rev. D

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138

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Maximally supersymmetric Yang-Mills theory in four dimensions can be formulated on a spacetime lattice while exactly preserving a single supersymmetry. Here we explore in detail this lattice theory, paying particular attention to its strongly coupled regime. Targeting a theory with gauge group SU(N ), the lattice formulation is naturally described in terms of gauge group U(N ). Although the U(1) degrees of freedom decouple in the continuum limit we show that these degrees of freedom lead to unwanted lattice artifacts at strong coupling. We demonstrate that these lattice artifacts can be removed, leaving behind a lattice formulation based on the SU(N ) gauge group with the expected apparently conformal behavior at both weak and strong coupling.

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Section: The Phase Of the Pfaffianmentioning

confidence: 99%

N=4supersymmetry on a space-time lattice

Catterall¹,

Schaich²,

Damgaard³

et al. 2014

Phys. Rev. D

Self Cite

138

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show abstract

“…the dimensional reduction of 4d N = 1 pure YM), there is no sign problem in the continuum limit. Although the complex phase appears as a lattice artifact [30,31], one can take the correct continuum limit without the complex phase by using the phase quenched ensemble [17,18,32].…”

Section: (No) Sign Problemmentioning

confidence: 99%

Monte Carlo approach to the string/M-theory

Hanada¹

2012

Proceedings of the 30th International Symposium on Lattice Field Theory — PoS(Lattice 2012)

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It has long been conjectured that certain supersymmetric Yang-Mills (SYM) theories provide us with nonperturbative formulations of the string/M-theory. Although the supersymmetry (SUSY) on lattice is notoriously difficult in general, for a class of theories important for the string/Mtheory various lattice and non-lattice methods, which enable us to study them on computers, have been proposed by now. In this talk, firstly I explain how SYM and string/M-theory are related. Then I explain why the lattice SUSY is difficult in general, and how the difficulties are solved in theories related to string/M-theory. Then I review the status of the simulation of the simulations. It is explained that some stringy effects are correctly incorporated in SYM. Furthermore, concrete values can be obtained from the SYM side, even when a direct calculation on the string theory side is impossible by the state-of-the-art techniques. We also comment on other recent developments, including the membrane mini-revolution in 2008 and simulation of the matrix model formulation of the string theory.

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“…5 A way to control them in lattice simulations is to introduce suitable gauge invariant, but Q non-invariant, potential terms (similar to the approach described in ref. [26]) by hand. Another point to note is that these theories might also suffer from fermion sign problem.…”

Section: Jhep07(2014)067mentioning

confidence: 97%

“…The next step is to extend this theory such that it becomes a supersymmetric quiver gauge theory with two nodes and 1 There also exist other complementary approaches to the problem of lattice supersymmetry [13][14][15][16][17][18][19][20][21][22]. 2 Several aspects of this theory have been explored numerically in the recent past [23][24][25][26][27][28][29][30] JHEP07 (2014)067 with gauge group SU(N c ) × SU(N f ). This can be achieved by replicating the continuum twisted theory and then changing the group representation of an appropriate subset of the field content of the theory from adjoint to the product representations (N c , N f ) and (N c , N f ), with N c and N f being the fundamental representations of SU(N c ) and SU(N f ) respectively.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional N $$ \mathcal{N} $$ = (2, 2) lattice gauge theories with matter in higher representations

Joseph

2014

J. High Energ. Phys.

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We construct two-dimensional N = (2, 2) supersymmetric gauge theories on a Euclidean spacetime lattice with matter in the two-index symmetric and anti-symmetric representations of SU(N c ) color group. These lattice theories preserve a subset of the supercharges exact at finite lattice spacing. The method of topological twisting is used to construct such theories in the continuum and then the geometric discretization scheme is used to formulate them on the lattice. The lattice theories obtained this way are gaugeinvariant, free from fermion doubling problem and exact supersymmetric at finite lattice spacing. We hope that these lattice constructions further motivate the nonperturbative explorations of models inspired by technicolor, orbifolding and orientifolding in string theories and the Corrigan-Ramond limit.

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On the sign problem in 2D lattice super Yang-Mills

Cited by 40 publications

References 52 publications

N=4supersymmetry on a space-time lattice

N=4supersymmetry on a space-time lattice

Monte Carlo approach to the string/M-theory

Two-dimensional N $$ \mathcal{N} $$ = (2, 2) lattice gauge theories with matter in higher representations

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