Wed·Oct 13, 2021Wednesday·October 13, 2021

1. 01*

   Clock model interpolation and symmetry breaking in O(2) models

   Leon Hostetler🇺🇸 · Jin Zhang🇺🇸 · Ryo Sakai🇺🇸 · Judah Unmuth-Yockey🇺🇸 · Alexei Bazavov🇺🇸 · Yannick Meurice🇺🇸

   The $q$-state clock model is a classical spin model that corresponds to the Ising model when $q=2$ and to the $XY$ model when $q\to \infty$. The integer-$q$ clock model has been studied extensively and has been shown to have a single phase transition when $q=2$,$3$,$4$ and two phase transitions when $q>4$.We define an extended $q$-state clock model that reduces to the ordinary $q$-state clock model when $q$ is an integer and otherwise is a continuous interpolation of the clock model to noninteger $q$. We investigate this class of clock models in 2D using Monte Carlo (MC) and tensor renormalization group (TRG) methods, and we find that the model with noninteger $q$ has a crossover and a second-order phase transition. We also define an extended-$O(2)$ model (with a parameter $\gamma$) that reduces to the $XY$ model when $\gamma =0$ and to the extended $q$-state clock model when $\gamma \to \infty$, and we begin to outline the phase diagram of this model. These models with noninteger $q$ serve as a testbed to study symmetry breaking in situations corresponding to quantum simulators where experimental parameters can be tuned continuously.

   hep-latcond-mat.stat-mechphysics.comp-phPoS(2022)·6 citations
2. 02*

   Tensor renormalization group and the volume independence in 2D U($N$) and SU($N$) gauge theories

   Mitsuaki Hirasawa🇯🇵 · Akira Matsumoto🇯🇵 · Jun Nishimura🇯🇵 · Atis Yosprakob🇯🇵

   The tensor renormalization group method is a promising approach to lattice field theories, which is free from the sign problem unlike standard Monte Carlo methods. One of the remaining issues is the application to gauge theories, which is so far limited to U(1) and SU(2) gauge groups. In the case of higher rank, it becomes highly nontrivial to restrict the number of representations in the character expansion to be used in constructing the fundamental tensor. We propose a practical strategy to accomplish this and demonstrate it in 2D U($N$) and SU($N$) gauge theories, which are exactly solvable. Using this strategy, we obtain the singular-value spectrum of the fundamental tensor, which turns out to have a definite profile in the large-$N$ limit. For the U($N$) case, in particular, we show that the large-$N$ behavior of the singular-value spectrum changes qualitatively at the critical coupling of the Gross-Witten-Wadia phase transition. As an interesting consequence, we find a new type of volume independence in the large-$N$ limit of the 2D U($N$) gauge theory with the $\theta$ term in the strong coupling phase, which goes beyond the Eguchi-Kawai reduction.

   hep-lathep-thJHEP(2021)·32 citations
3. 03*

   Cluster expansion and resurgence in Polyakov model

   Cihan Pazarbaşı🇹🇷 · Mithat Ünsal🇺🇸

   In Polyakov model, a non-perturbative mass gap is formed at leading order semi-classics by instanton effects. By using the notions of critical points at infinity, cluster expansion and Lefschetz thimbles, we show that a third order effect in semi-classics gives an imaginary ambiguous contribution to mass gap, which is supposed to be real and unambiguous. This is troublesome for the original analysis, and it is difficult to resolve this issue directly in QFT. However, we find a new compactification of Polyakov model to quantum mechanics, by using a background 't Hooft flux (or coupling to TQFT). The compactification has the merit of remembering the monopole-instantons of the full QFT within Born-Oppenheimer (BO) approximation, while the periodic compactification does not. In QM, we prove the resurgent cancellation of the ambiguity in 3-instanton sector against ambiguity in the Borel resummation of the perturbation theory around 1-instanton. Assuming that this result holds in QFT, we provide a large-order asymptotics of perturbation theory around perturbative vacuum and instanton.

   ↳ hep-thhep-latPRL(2022)·7 citations
4. 04*

   On the AdS/CFT correspondence and quantum entanglement

   Badis Ydri🇩🇿

   String theory provides one of the most deepest insights into quantum gravity. Its single most central and profound result is the gauge/gravity duality, i.e. the emergence of gravity from gauge theory. The two examples of M(atrix)-theory and the AdS/CFT correspondence, together with the fundamental phenomena of quantum entanglement, are of paramount importance to many fundamental problems including the physics of black holes (in particular to the information loss paradox), the emergence of spacetime geometry and to the problem of the reconciliation of general relativity and quantum mechanics. In this article an account of the AdS/CFT correspondence and the role of quantum entanglement in the emergence of spacetime geometry using strictly the language of quantum field theory is put forward.

   ↳ hep-thhep-exhep-lathep-ph3 citations
5. 05*

   Light-cone distribution amplitudes of the nucleon and $\Delta$ baryon

   June-Young Kim🇩🇪 · Hyun-Chul Kim🇰🇷 · Maxim V. Polyakov🇩🇪

   We investigate the light-cone wave functions and leading-twist distribution amplitudes for the nucleon and $\Delta$ baryon within the framework of the chiral quark-soliton model. The baryon wave function consists of the valence quark and vacuum wave functions. The vacuum wave functions generate all possible higher Fock states by expanding them. We find that it is essential to consider the five-quark component and relativistic corrections to evaluate the distribution amplitudes of the nucleon and $\Delta$ isobar. Having taken into account them, we derive the distribution amplitudes. The results are in good agreement with the lattice data.

   ↳ hep-phhep-latJHEP(2021)·12 citations
6. 06*

   Padé approximants to $B\to \pi \ell {\nu }_{\ell }$ and $B_s\to K\ell {\nu }_{\ell }$ and determination of $|V_{ub}|$

   Sergi Gonzàlez-Solís🇺🇸 · Pere Masjuan🇪🇸 · Camilo Rojas🇪🇸

   In light of the first observation of the semileptonic decay $B_s^0\to K^{-}{\mu }^{+}{\nu }_{\mu }$ by the LHCb collaboration, we revisit the determination of the CKM parameter $|V_{ub}|$ from exclusive semileptonic $B$-meson decays. A controlled theoretical input on the Standard Model $B\to \pi$ and $B_s\to K$ vector and scalar form factors from Lattice QCD in the large $q^2$ region, in combination with experimental measurements of the differential $B\to \pi \ell {\nu }_{\ell }$ and $B_s^0\to K^{-}{\mu }^{+}{\nu }_{\mu }$ branching ratio distributions, has allowed us determine $|V_{ub}|=3.86(11)\times 10^{-3}$ and $|V_{ub}|=3.58(9)\times 10^{-3}$ from the analyses of the individual decay channels, respectively, and $|V_{ub}|=3.68(5)\times 10^{-3}$ from a simultaneous analysis of both decays, which is only a $1.4\%$ error and differs by $1.8\sigma$ with respect to the value from inclusive determinations $|V_{ub}|=4.25(12{)}_{-14}^{+15}(23)\times 10^{-3}$. Our results are based on the use of Padé approximants to the participating form factors, highlight the importance of the decay $B_s\to K\mu {\nu }_{\mu }$ in complementing the traditional $B\to \pi \ell {\nu }_{\ell }$ one in the exclusive determination of $|V_{ub}|$, and allow obtain, to the best of our knowledge, the first correlated results for the $B\to \pi$ and $B_s\to K$ vector and scalar form factors. We hope that our study strengthens the case for precise measurements of the differential $B_s\to K\ell {\nu }_{\ell }$ decay rate with a finer resolution of the $q^2$ bins, as it would definitely allow achieving more conclusive results for $|V_{ub}|$.

   ↳ hep-phhep-exhep-latPRD(2021)·20 citations

* Reconstructed cohort: no mailing for this day survives in the archive. Papers are grouped by their submission times and arXiv's announcement cut-off, assuming announcement without delay; positions follow identifier order. Validated at ~91% exact-day agreement against the archived era.