Twisted supersymmetric sigma model on the lattice

Catterall, Simon; Ghadab, Sofiane

doi:10.1088/1126-6708/2006/10/063

Cited by 27 publications

(26 citation statements)

References 56 publications

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“…In the case of Yang-Mills theories it appears that these approaches are intimately connected [23,24]. The approach based on twisting has also been studied in the case of Wess-Zumino and sigma models [25,26,27,28,29]. The philosophy behind these approaches is that this residual lattice supersymmetry will help to protect the theory from the dangerous radiative corrections which lead to fine tuning.…”

Section: Introductionmentioning

confidence: 99%

Towards lattice simulation of the gauge theory duals to black holes and hot strings

Catterall

Wiseman

2007

J. High Energy Phys.

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115

101

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Abstract:A generalization of the AdS/CFT conjecture postulates a duality between IIA string theory and 16 supercharge Yang-Mills quantum mechanics in the large N 't Hooft limit. At low temperatures string theory describes black holes, whose thermodynamics may hence be studied using the dual quantum mechanics. This quantum mechanics is strongly coupled which motivates the use of lattice techniques. We argue that, contrary to expectation, the theory when discretized naively will nevertheless recover continuum supersymmetry as the lattice spacing is sent to zero. We test these ideas by studying the 4 supercharge version of this Yang-Mills quantum mechanics in the 't Hooft limit. We use both a naive lattice action and a manifestly supersymmetric action. Using Monte Carlo methods we simulate the Euclidean theories, and study the lattice continuum limit, for both thermal and non-thermal periodic boundary conditions, confirming continuum supersymmetry is recovered for the naive action when appropriate. We obtain results for the thermal system with N up to 12. These favor the existence of a single deconfined phase for all non-zero temperatures. These results are an encouraging indication that the 16 supercharge theory is within reach using similar methods and resources.arXiv:0706.3518v1 [hep-lat]

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Section: Introductionmentioning

confidence: 99%

Towards lattice simulation of the gauge theory duals to black holes and hot strings

Catterall

Wiseman

2007

J. High Energy Phys.

Self Cite

115

101

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“…However, one might hope that this symmetry along with the other supersymmetry is restored in the continuum limit (large β) where the fields vary slowly over the lattice. There is some evidence for this in the analogous two dimensional sigma models [101]. It would be very interesting to investigate this in more detail in this simpler one dimensional case.…”

Section: Sigma Modelsmentioning

confidence: 87%

“…In the case of a curved target space we must add the Wilson term in the form of a twisted mass term rather than a superpotential. We refer to [101] for details. This breaks the Q symmetry softly although numerical results still favor the restoration of full supersymmetry without fine tuning in the continuum limit [101].…”

Section: Sigma Modelsmentioning

confidence: 99%

Exact lattice supersymmetry☆

Catterall¹,

Kaplan²,

Ünsal³

2008

Journal of End-to-End-testing

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We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of N = 4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems.

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“…By construction this action is invariant under supersymmetries generated by Q. This approach has been applied to the O(3)-NLSM in [13,14]. However, the authors employ a formulation of the model in terms of unconstrained fields and its discretization breaks the O(3) symmetry in such a way that it is not restored in the continuum limit.…”

Section: Supersymmetries On the Latticementioning

confidence: 99%

“…Having encountered these problems in the simple bosonic case, we ought to be very careful with a discretization of the superymmetric model and should always check the restoration of the O(3) symmetry. Unfortunately this was not done in [13,14] and we shall see below that this symmetry is actually broken in the lattice models constructed by Catterall and Ghadab. The formulation in [13,14] is based on a Q-exact deformation of the O(3) sigma model in the unconstrained CP 1 formulation.…”

Section: Drawbacks Of a Q-exact Lattice Formulationmentioning

confidence: 99%

Supersymmetric nonlinear O(3) sigma model on the lattice

Flore

Körner

Wipf

et al. 2012

J. High Energ. Phys.

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A supersymmetric extension of the nonlinear O(3) sigma model in two spacetime dimensions is investigated by means of Monte Carlo simulations. We argue that it is impossible to construct a lattice action that implements both the O(3) symmetry as well as at least one supersymmetry exactly at finite lattice spacing. It is shown by explicit calculations that previously proposed discretizations fail to reproduce the exact symmetries of the target manifold in the continuum limit. We provide an alternative lattice action with exact O(3) symmetry and compare two approaches based on different derivative operators. Using the nonlocal SLAC derivative for the quenched model on moderately sized lattices we extract the value σ(2, u 0 ) = 1.2604(13) for the step scaling function at u 0 = 1.0595, to be compared with the exact value 1.261210. For the supersymmetric model with SLAC derivative the discrete chiral symmetry is maintained but we encounter strong sign fluctuations, rendering large lattice simulations ineffective. By applying the Wilson prescription, supersymmetry and chiral symmetry are broken explicitly at finite lattice spacing, though there is clear evidence that both are restored in the continuum limit by fine tuning of a single mass parameter.

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Twisted supersymmetric sigma model on the lattice

Cited by 27 publications

References 56 publications

Towards lattice simulation of the gauge theory duals to black holes and hot strings

Towards lattice simulation of the gauge theory duals to black holes and hot strings

Exact lattice supersymmetry☆

Supersymmetric nonlinear O(3) sigma model on the lattice

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