(Phenomenology/Lattice-Compatible) SU(3) MχPT HD up to $$ \mathcal{O} $$(p4) and the $$ \mathcal{O} $$(R4)-Large-N Connection

Abstract

Obtaining the values of the coupling constants of the low energy effective theory corresponding to QCD, compatible with experimental data, even in the (vector) mesonic sector from (the $$ \mathcal{M} $$ M -theory uplift of) a UV-complete string theory dual, has thus far been missing in the literature. We take the first step in this direction by obtaining the values of the coupling constants of the $$ \mathcal{O} $$ O (p4) χPT Lagrangian in the chiral limit involving the NGBs and ρ meson (and its flavor partners) from the $$ \mathcal{M} $$ M -theory/type IIA dual of large-N thermal QCD, inclusive of the $$ \mathcal{O} $$ O (R4) corrections. We observe that ensuring compatibility with phenomenological/lattice results (the values) as given in [1], requires a relationship relating the $$ \mathcal{O} $$ O (R4) corrections and large-N suppression. In other words, QCD demands that the higher derivative corrections and the large-N suppressed corrections in its M/string theory dual, are related. As a bonus, we explicitly show that the $$ \mathcal{O} $$ O (R4) corrections in the UV to the $$ \mathcal{M} $$ M -theory uplift of the type IIB dual of large-N thermal QCD at low temperatures, can be consistently set to be vanishingly small.

ℳcTEQ (ℳ chiral perturbation theory-compatible deconfinement Temperature and Entanglement Entropy up to terms Quartic in curvature) and FM (Flavor Memory)

“…Numerically, choosing N = 100, M UV = N UV f = 0.01, M = N f = 3, α θ 1,2 : α 3 θ 1 α 2 θ 2 = 2, and r 0 = N − fr 0 3 , f r 0 ≈ 1 [1], one obtains the plots in figure 2. Let us also discuss the possibility of r * ∈ [r 0 , R D5/D5 ], i.e., IR-valued r * and splitting…”

“…Starting with M -theory dual of thermal QCD-like theories in the 'MQGP' limit as constructed in [3] and incorporating higher derivative terms in eleven dimensional supergravity action which are quartic in Riemann curvature tensor i.e. O(R 4 ), the corrections to the supergravity background were then worked out in [11] and in fact, successfully used in [1] in obtaining phenomenologically-compatible values of the NLO LECs in SU(3) χPT Lagrangian of [5].…”

“…Section 7 has a summary of the results obtained in the paper. There is a supplementary appendix on the EOMs and solutions to the O(R 4 ) metric corrections to the MQGP background of [3,4], as well as a discussion on taking the decompactification-limit of a periodic spatial direction in the thermal background M -theory uplift used in [1] to obtain the M -theory thermal background in this paper, and deriving the sign of a linear combination of constants of integration in the solutions to the EOMs of the O(R 4 )M -theory metric corrections as required from matching of results of [1] with phenomenological values of the LECs at NLO in the SU(3) χPT Lagrangian of [5].…”

“…In [1], we worked out one-loop renormalised LECs of SU(3) chiral perturbation theory Lagrangian up to O(p 4 ) from type IIA string dual of large-N thermal QCD like-theory inclusive of O(R 4 ) corrections. We constrained ourselves to the chiral limit due to which some terms were absent in SU(3) chiral perturbation theory Lagrangian of Gasser and Leutwyler [5].…”

“…The aforementioned linear combination of O(R 4 ) corrections to the M -theory uplift [3,4] metric, upon matching the holographic result from M χPT [1] with the phenomenological value of the coupling constant of one of the SU(3) NLO χPT Lagrangian of [5], is required to have a definite sign. Interestingly, in the decompactification (or "M KK → 0") limit of the spatial circle in [1] to recover a QCD-like theory in four dimensions after integrating out the compact directions, we not only derive this, but in fact obtain the values of the relevant O(R 4 ) metric corrections. Further, equivalence with Wald entropy for the black hole in the high-temperature M -theory dual at O(R 4 ) imposes a linear constraint on a similar linear combination of the abovementioned metric corrections.…”