To gauge or not to gauge?

Maldacena, Juan; Milekhin, Alexey

doi:10.1007/jhep04(2018)084

Cited by 60 publications

(103 citation statements)

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“…We indeed observe a rather good agreement within a few percent accuracy for the temperature dependence of both the energy and the coordinate dispersion for all simulation parameters used in [41]. It is also interesting to note that the Gaussian state approximation also reproduces very precisely the prediction of [52] for the low-temperature behavior of the energy of the ungauged model. Expanding the equations (24) and (23) to the leading order in f − 1/2, it is easy to obtain the lowtemperature asymptotics of the equation of state…”

Section: A Bosonic Matrix Modelsupporting

confidence: 70%

“…As a consequence, our simulations correspond to the ungauged version of the BFSS or bosonic matrix models, where no gauge constraints are imposed on the state vectors. Fortunately, the differences between the gauged and ungauged models appear to be minor at least at low temperatures, as conjectured recently in [52] and demonstrated numerically in [41]. Yet another argument in favor of accuracy of the Gaussian state approximation is that, as we will demonstrate, it reproduces the numerical results for the equation of state of the ungauged bosonic matrix model [41] within a few percent accuracy all the way from low to high temperatures.…”

Section: Introductionsupporting

confidence: 71%

“…Fortunately, as discussed recently in [41,52], the physics of the bosonic matrix model and the BFSS model does not strongly depend on gauging. More precisely, gauged and ungauged theories are expected to be the same up to the e −C/T correction at low temperature, where C is an order one constant.…”

Section: Gaussian State Approximation For the Real-time Dynamicsmentioning

confidence: 88%

“…In contrast to the full BFSS model, at low temperatures the bosonic matrix model is expected to be in the confinement regime [54] with finite groundstate energy. While in the ungauged bosonic matrix model there is no strict notion of confinement and the high-and low-temperature regimes appear to be smoothly connected, at sufficiently low temperatures physical observables in the gauged and in the ungauged models become exponentially close [41,52].…”

Section: Gaussian State Approximation For the Real-time Dynamicsmentioning

confidence: 99%

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Quantum chaos, thermalization, and entanglement generation in real-time simulations of the Banks-Fischler-Shenker-Susskind matrix model

2019

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We study numerically the onset of chaos and thermalization in the Banks-Fischler-Shenker-Susskind (BFSS) matrix model with and without fermions, considering Lyapunov exponents, entanglement generation, and quasinormal ringing. We approximate the real-time dynamics in terms of the most general Gaussian density matrices with parameters which obey self-consistent equations of motion, thus extending the applicability of real-time simulations beyond the classical limit. Initial values of these Gaussian density matrices are optimized to be as close as possible to the thermal equilibrium state of the system. Thus attempting to bridge between the low-energy regime with a calculable holographic description and the classical regime at high energies, we find that quantum corrections to classical dynamics tend to decrease the Lyapunov exponents, which is essential for consistency with the Maldacena-Shenker-Stanford (MSS) bound at low temperatures. The entanglement entropy is found to exhibit an expected "scrambling" behavior -rapid initial growth followed by saturation. At least at high temperatures the entanglement saturation time appears to be governed by classical Lyapunov exponents. Decay of quasinormal modes is found to be characterized by the shortest time scale of all. We also find that while the bosonic matrix model becomes nonchaotic in the low-temperature regime, for the full BFSS model with fermions the leading Lyapunov exponent, entanglement saturation time, and decay rate of quasinormal modes all remain finite and non-zero down to the lowest temperatures.

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Section: A Bosonic Matrix Modelsupporting

confidence: 70%

Section: Introductionsupporting

confidence: 71%

Section: Gaussian State Approximation For the Real-time Dynamicsmentioning

confidence: 88%

Section: Gaussian State Approximation For the Real-time Dynamicsmentioning

confidence: 99%

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Quantum chaos, thermalization, and entanglement generation in real-time simulations of the Banks-Fischler-Shenker-Susskind matrix model

2019

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“…[21 -26]. Another illustration is a recent proposal [27] that 'ungauging' Q = 16 SYM QM (to consider a scalar-fermion system with SU(N ) global symmetry) has relatively little effect, in the sense that both the gauged and ungauged models flow to the same theory in the IR. This conjecture was quickly tested by lattice calculations that found consistent results [28].…”

Section: +1 Dimensionsmentioning

confidence: 99%

Progress and prospects of lattice supersymmetry

Schaich¹

2019

Proceedings of the 36th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2018)

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Supersymmetry plays prominent roles in the study of quantum field theory and in many proposals for potential new physics beyond the standard model, while lattice field theory provides a nonperturbative regularization suitable for strongly interacting systems. Lattice investigations of supersymmetric field theories are currently making significant progress, though many challenges remain to be overcome. In this brief overview I discuss particularly notable progress in three areas: supersymmetric Yang-Mills (SYM) theories in fewer than four dimensions, as well as both minimal N = 1 SYM and maximal N = 4 SYM in four dimensions. I also highlight super-QCD and sign problems as prominent challenges that will be important to address in future work. Progress and prospects of lattice supersymmetry David Schaich Introduction, motivation and backgroundSupersymmetry plays prominent roles in modern theoretical physics, as a tool to improve our understanding of quantum field theory (QFT), as an ingredient in many new physics models, and as a means to study quantum gravity via holographic duality. Lattice field theory provides a nonperturbative regularization for QFTs, and other contributions to these proceedings document the prodigious success of this framework applied to QCD and similar theories. It is natural to consider employing lattice field theory to investigate supersymmetric QFTs, especially in strongly coupled regimes. In this proceedings I review the recent progress and future prospects of lattice studies of supersymmetric systems, focusing on four-dimensional gauge theories and their dimensional reductions to d < 4. 1 Lattice supersymmetry now has more than four decades of history [1], much of which is reviewed by Refs. [2 -7]. Unfortunately, progress in this field has been slower than for QCD, in large part because the lattice discretization of space-time breaks supersymmetry. This occurs in three main ways. First, the anti-commutation relation Q α , Qα = 2σ µ αα P µ in the super-Poincaré algebra connects the spinorial generators of supersymmetry transformations, Q α and Qα, to the generator of infinitesimal space-time translations, P µ . The absence of infinitesimal translations on the lattice consequently implies broken supersymmetry.Next, bosonic and fermionic fields are typically discretized differently on the lattice (in part due to the famous fermion doubling problem). In the specific context of supersymmetric gauge theories, standard discretizations associate the gauginos with lattice sites n (i.e., they transform as G(n)λ α (n)G † (n) under a lattice gauge transformation) while the gauge connections are associated with links between nearest-neighbor sites, transforming as G(n)U µ (n)G † (n + a µ) where 'a' is the lattice spacing. Away from the a → 0 continuum limit, these differences prevent supersymmetry transformations from correctly interchanging superpartners.Finally, supersymmetry requires a derivative operator that obeys the Leibniz rule [1], viz. ∂ [φη] = [∂φ] η + φ∂η, which is violated by standard la...

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Matrix Models and Non‐Abelian T Dual of AdS5×S5$AdS_5 \times S^5$

Roychowdhury

2023

Fortschritte der Physik

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Euclidean Wilson loops for BMN Plane Wave Matrix Models is computed. The stringy counterpart of these Wilson loops corresponds to various semi‐classical open string embedding that probe a class of half BPS geometries in Type IIA supergravity. These geometries fall under the general category of Lin‐Lunin and Maldacena (LLM). As a special class of solutions within the LLM category, Wilson operators corresponding to the non‐Abelian T dual (NATD) of is constructed. The analysis shows close agreement between matrix model and string theory calculations.

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To gauge or not to gauge?

Cited by 60 publications

References 50 publications

Quantum chaos, thermalization, and entanglement generation in real-time simulations of the Banks-Fischler-Shenker-Susskind matrix model

Quantum chaos, thermalization, and entanglement generation in real-time simulations of the Banks-Fischler-Shenker-Susskind matrix model

Progress and prospects of lattice supersymmetry

Matrix Models and Non‐Abelian T Dual of AdS5×S5$AdS_5 \times S^5$

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