Improved lattice actions for supersymmetric quantum mechanics

Schierenberg, Sebastian; Bruckmann, Falk

doi:10.1103/physrevd.89.014511

Cited by 8 publications

(8 citation statements)

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“…See [64,65] for the restoration of supersymetry in the continuum limit, [66] for the RG flow, [67] for a use of the Nicolai map and the relation to a certain superconformal minimal model, [68] for an improvement of the lattice actions of the matrix quantum mechanics, and [69,37] for the spontaneous SUSY breaking.…”

Section: Other Topicsmentioning

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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Section: Other Topicsmentioning

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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“…[7] in an approach that combined canonical and path integral approaches ). Lattice studies [17] use the Nicolai map but, apparently, do not consider the stochastic identities themselves. These are "broken" by the lattice since the auxiliary field has a local propagator, that becomes ultra-local only in the continuum limit (at least for the free theory).…”

Section: Discussionmentioning

confidence: 99%

Supersymmetric probability distributions

Nicolis¹,

Zerkak²

2013

J. Phys. A: Math. Theor.

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We use anticommuting variables to study probability distributions of random variables, that are solutions of Langevin's equation. We show that the probability density always enjoys "worldpoint supersymmetry". The partition function, however, may not. We find that the domain of integration can acquire a boundary, that implies that the auxiliary field has a non-zero expectation value, signalling spontaneous supersymmetry breaking. This is due to the presence of "fermionic" zeromodes, whose contribution cannot be cancelled by a surface term. This we prove by an explicit calculation of the regularized partition function, as well as by computing the moments of the auxiliary field and checking whether they satisfy the identities implied by Wick's theorem. Nevertheless, supersymmetry manifests itself in the identities that are satisfied by the moments of the scalar, whose expressions we can calculate, for all values of the coupling constant. We also provide some quantitative estimates concerning the visibility of supersymmetry breaking effects in the identities for the moments and remark that the shape of the distribution of the auxiliary field can influence quite strongly how easy it would be to mask them, since the expectation value of the auxiliary field doesn't coincide with its typical value.

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“…A systematic modification might be possible in the context of Section II B or as an approximate solution of the additional constraint. Such an approximation can be compared with the truncations of the nonlocal solutions of the naive symmetry relation as derived in [18].…”

Section: Translational Invariance Blockedmentioning

confidence: 99%