Search arXiv⌕ Search

arXiv · 0710.0704

Triage of the Sign Problem

Abstract

We discuss the sign problem in QCD at nonzero chemical potential and its relation with chiral symmetry breaking and the spectrum of the Dirac operator using the framework of chiral random matrix theory. We show that the Banks-Casher formula is not valid for theories with a sign problem and has to be replaced by an alternative mechanism that is worked out in detail for QCD in one dimension at nonzero chemical potential.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

K. Splittorff, J. J. M. Verbaarschot. 2007-10-03. Triage of the Sign Problem. https://arxiv.org/abs/0710.0704

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Time-like Janus Solution -- holographic global quantum quench --

We construct a time-like Janus solution, which is mediated by a time-dependent dilaton field in asymptotic AdS spacetime. This solution breaks the null energy condition, but we argue that it is nevertheless useful as a toy model of holographic global quantum quench. The dual CFT is given by conformal perturbation theory, where the primary scalar operator that is dual to the bulk dilaton field is coupled with a global-quench-type time-dependent source. We compute one-point functions of the scalar operator and the stress-energy tensor, and confirm that the results are consistent with the proposed CFT picture. We also evaluate the holographic entanglement entropy for late time after the global quench. Finite temperature version of the solution, which can be interpreted as a time-dependent black hole, is also discussed.

hep-th↗

ADE Minimal Strings and Multi-Matrix Duals

We revisit ADE minimal string theories, focusing on the D- and E-series minimal models coupled to Liouville theory. Unlike the A-series, whose duals are solvable two-matrix models, these theories are conjectured to correspond to unsolvable four-matrix integrals. We compute sphere four-point and torus one-point amplitudes in the AMS, DMS, and EMS via direct numerical integration over moduli space, confirming/disproving some known results and providing new data where matrix-model predictions are unavailable. For torus one-point amplitudes, we also present conjectural analytic formulas consistent with all our numerical checks. From amplitudes with conformal boundaries, we find evidence for multi-matrix structure in the D-series, including scaled ramp behavior in cylinder diagrams and deviations from the ZZ-instanton sector of two-matrix models. We also perform a preliminary positivity bootstrap to constrain critical points of the multi-matrix models relevant to the DMS string.

hep-th↗

Resurgence in the Virasoro Minimal String and 3d Gravity

We compute non-perturbative, resurgent contributions to the Virasoro minimal string and 3d gravity using techniques from hermitian matrix models. In particular, we construct a fully non-perturbative partition function for the Virasoro minimal string in terms of a Zak transform. In this context, negative tension D-branes appear naturally, which in the matrix model correspond to anti-eigenvalues, or instantons on the involuted sheet of the spectral curve. We further extend this analysis to resolvents and observe resurgent wall crossing phenomena between ZZ- and FZZT-branes. Using recent results that relate the Virasoro minimal string to 3d gravity with end-of-the-world branes we proceed to study the resurgent consequences of summing over the genus in 3d gravity, where we find non-perturbative contributions of doubly exponential type. These statements are then tested using resurgent large-order asymptotics. Lastly, we compute the non-perturbative eigenvalue density for generic hermitian matrix models and identify the change of asymptotic behavior at the edge of the eigenvalue distribution with a Stokes transition. This allows us to identify oscillations in the eigenvalue density with anti-Stokes behavior of FZZT-branes. In the case of 3d gravity with end-of-the-world branes we comment how this Stokes transition coincides with the onset of black hole behaviour and compute the non-perturbative primary density. Furthermore, we apply these techniques to the eigenvalue density of JT gravity to compute higher genus corrections.

hep-th↗