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$T_c$, Photoproduction, Paramagnetic Anisotropic Plasma, IR Log-Gravitational-DBI Renormalization and $G_2$-Structure Induced (Almost) Contact 3-Structures in Hot Strongly Magnetic MQCD at Intermediate Coupling

Shivam Singh Kushwah, Aalok Misra

TL;DR

The paper develops a top-down holographic model of hot QCD-like matter at intermediate coupling under strong magnetic fields, using the MQGP uplift and D6-brane world-volume DBI actions. It computes the photoproduction spectral function including ${\cal O}(R^4)$ corrections and analyzes a generalized EoS derived from the DBI action, identifying IR log-renormalization via a boundary ${\log\det\mathrm{Ricci}}$ term and UV non-renormalization in a self-consistent truncation. It shows that a strong magnetic field lowers the deconfinement temperature $T_c$ and argues, from the EoS, that the preferred high-temperature phase is a paramagnetic, pressure/energy-anisotropic plasma with wormhole- and phantom-energy-inspired interpretations; it also relates AC3S/C3S structures to the analytic structure of the complexified gauge coupling. The work connects holographic photoproduction and generalized EoS to precise geometric structures arising from ${G_2}$ and almost-contact 3-structures, providing a coherent framework for magnetized QGP at intermediate coupling with potential implications for heavy-ion phenomenology and neutron-star physics.

Abstract

After obtaining the flavor $D6$-brane gauge fields/their fluctuations in the type IIA dual of T>T_c QCD-like theories at intermediate coupling (via the ${\cal M}$-theory uplift's ${\cal O}(R^4)$ corrections) in the absence/presence of a strong magnetic field, we compute the photoproduction spectral function and get a nice agreement with gauged supergravity backgrounds arXiv:2204.00024 [hep-th]. We demonstrate from the EoS that the holographic dual, in principle, could correspond to several $T>T_c$ scenarios: anisotropic paramagnetic plasma transitioning via a smooth crossover to exotic matter as the universe cools, the stable wormhole, and a paramagnetic pressure/energy-anisotropic plasma. Given that $T>T_c$ QGP is expected to be paramagnetic, see Bali et al '14, the third possibility appears to be the preferred one. We also show that it is not possible that the anisotropic plasma leads to the formation of a compact star. IR renormalization of the DBI action requires a boundary Log-det-Ricci-tensor counter term. {\it Noting (i) photoproduction spectral function determined from gauge field fluctuations receiving ${\cal O}(R^4)$-corrections, if complexified, include a non-analytic-complexified gauge-coupling dependence, and correspond to Contact 3-Structures; (ii) pressure/energy density, etc. determined from world-volume gauge fields and not ${\cal O}(R^4)$-corrected, if complexified, are analytic in the complexified gauge coupling, and correspond to Almost Contact 3-Structures (AC3S) both induced from the $G_2$ structure of a closed seven-fold, we conjecture (i) the lack of $N$-path connectedness in the parameter space associated with AC3S and C3S arXiv:2211.13186[hep-th] to be equivalent to that gauge field fluctuations can not be finite, and (zero-instanton sector) ${\cal O}(R^4)$ non-renormalized gauge fields produce ${\cal O}(R^4)$-corrected gauge fluctuation; (ii) C3S--UV--> AC3S.

$T_c$, Photoproduction, Paramagnetic Anisotropic Plasma, IR Log-Gravitational-DBI Renormalization and $G_2$-Structure Induced (Almost) Contact 3-Structures in Hot Strongly Magnetic MQCD at Intermediate Coupling

TL;DR

The paper develops a top-down holographic model of hot QCD-like matter at intermediate coupling under strong magnetic fields, using the MQGP uplift and D6-brane world-volume DBI actions. It computes the photoproduction spectral function including corrections and analyzes a generalized EoS derived from the DBI action, identifying IR log-renormalization via a boundary term and UV non-renormalization in a self-consistent truncation. It shows that a strong magnetic field lowers the deconfinement temperature and argues, from the EoS, that the preferred high-temperature phase is a paramagnetic, pressure/energy-anisotropic plasma with wormhole- and phantom-energy-inspired interpretations; it also relates AC3S/C3S structures to the analytic structure of the complexified gauge coupling. The work connects holographic photoproduction and generalized EoS to precise geometric structures arising from and almost-contact 3-structures, providing a coherent framework for magnetized QGP at intermediate coupling with potential implications for heavy-ion phenomenology and neutron-star physics.

Abstract

After obtaining the flavor -brane gauge fields/their fluctuations in the type IIA dual of T>T_c QCD-like theories at intermediate coupling (via the -theory uplift's corrections) in the absence/presence of a strong magnetic field, we compute the photoproduction spectral function and get a nice agreement with gauged supergravity backgrounds arXiv:2204.00024 [hep-th]. We demonstrate from the EoS that the holographic dual, in principle, could correspond to several scenarios: anisotropic paramagnetic plasma transitioning via a smooth crossover to exotic matter as the universe cools, the stable wormhole, and a paramagnetic pressure/energy-anisotropic plasma. Given that QGP is expected to be paramagnetic, see Bali et al '14, the third possibility appears to be the preferred one. We also show that it is not possible that the anisotropic plasma leads to the formation of a compact star. IR renormalization of the DBI action requires a boundary Log-det-Ricci-tensor counter term. {\it Noting (i) photoproduction spectral function determined from gauge field fluctuations receiving -corrections, if complexified, include a non-analytic-complexified gauge-coupling dependence, and correspond to Contact 3-Structures; (ii) pressure/energy density, etc. determined from world-volume gauge fields and not -corrected, if complexified, are analytic in the complexified gauge coupling, and correspond to Almost Contact 3-Structures (AC3S) both induced from the structure of a closed seven-fold, we conjecture (i) the lack of -path connectedness in the parameter space associated with AC3S and C3S arXiv:2211.13186[hep-th] to be equivalent to that gauge field fluctuations can not be finite, and (zero-instanton sector) non-renormalized gauge fields produce -corrected gauge fluctuation; (ii) C3S--UV--> AC3S.

Paper Structure

This paper contains 35 sections, 191 equations, 10 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Photo-production in top-down holographic QGP
  3. Study of generalized EoS
  4. Type IIB/IIA Dual of Large-$N$ Thermal QCD-Like Theories, its ${\cal M}$-Theory Uplift and the MQGP Limit
  5. ${\cal O}(l_p^6)$ Corrections and When to Go Beyond
  6. ${\cal O}(l_p^6)$ terms in ${\cal N}=1, D=11$ Supergravity Action
  7. When ${\cal O}(l_p^6)$ Is (Not) Enough
  8. Almost Contact 3-Structures Arising from $G_2$ Structure in the ${\cal M}$ Uplift in the Limit (\ref{['MQGP_limit']})
  9. $D6$-Branes' Gauge Fields in the Absence of Magnetic Fields in the IR/UV
  10. $A_\mu, \mu = t, \rho, \phi, Z, x^3$ in the IR Up to ${\cal O}(\beta^0)$
  11. Non-Renormalization in the IR Up to ${\cal O}(R^4)$ of $A_\mu, \mu=t, \rho, \phi, Z, x^3$
  12. $A_\mu, \mu = t, \rho, \phi, Z, x^3$ in the UV Up to ${\cal O}(\beta^0)$
  13. Non-Renormalization in the UV of $A_{\mu = t, \rho, \phi, Z, x^3}$ up to ${\cal O}(R^4)$ in the Self-Consistent truncation $A^\beta_{\mu = \rho, \phi, Z, x^3}=0$
  14. $D6$-Branes' Gauge Fields in the Presence of Strong Magnetic Fields
  15. In the IR
  16. ...and 20 more sections

Figures (10)

  • Figure 1: The Status of the Type IIB/IIA/${\cal M}$-theory dual of large-N QCD at high temperature metrics, MQGP, NPB inclusive of ${\cal O}(R^4)$ M-theory corrections OR4; $T^{1,1}_{NE}$ denotes a non-Einsteinian deformation of $T^{1,1}$
  • Figure 2: A smooth crossover from anisotrpioc plasma to exotic matter as the universe cools (defined in terms of "boundary time" (\ref{['rh-tb-relation']})) but stays above $T_c$: ${\cal C}_{\rm combo}\approx 0.33, {\cal C}^{(2)}_{\rm combo}=-1, {\cal C}_{x^3}^B(x^3) = 1$
  • Figure 3: Anisotropic plasma: ${\cal C}_{\rm combo} =- 1, {\cal C}^{(2)}_{\rm combo}=1, {\cal C}_{x^3}^B(x^3) = -0.001, B = 1 \left({\rm GeV}\right)^4;\ \tilde{t}\equiv\frac{T}{T_c}$
  • Figure 4: Anisotropic plasma: ${\cal C}_{\rm combo} =- 1, {\cal C}^{(2)}_{\rm combo}=1, {\cal C}_{x^3}^B(x^3) = -0.001;\ \tilde{t}\equiv\frac{T}{T_c}$
  • Figure 5: Anisotropic plasma: ${\cal C}_{\rm combo} =- 1, {\cal C}^{(2)}_{\rm combo}=100, {\cal C}_{x^3}^B(x^3) = -0.001;\ \tilde{t}\equiv\frac{T}{T_c}$
  • ...and 5 more figures