The Future of Thermal QCD Phenomenology at Intermediate Gauge/'t Hooft Coupling

Table of Links

Abstract

Acknowledgment

PART I

Chapter 1: Introduction

Chapter 2: SU(3) LECs from Type IIA String Theory

Chapter 3: Deconfinement Phase Transition in Thermal QCD-Like Theories at Intermediate Coupling in the Absence and Presence of Rotation

Chapter 4: Conclusion and Future Outlook

PART II

Chapter 5: Introduction

Chapter 6: Page Curves of Reissner-Nordström Black Hole in HD Gravity

Chapter 7: Entanglement Entropy and Page Curve from the M-Theory Dual of Thermal QCD Above Tc at Intermediate Coupling

Chapter 8: Black Hole Islands in Multi-Event Horizon Space-Times

Chapter 9: Multiverse in Karch-Randall Braneworld

Chapter 10: Conclusion and Future outlook

APPENDIX A

APPENDIX B

APPENDIX C

Bibliography

CHAPTER 4 - CONCLUSION AND FUTURE OUTLOOK

We explored the intermediate coupling regime of thermal QCD-like theories from a top-down model constructed in [1]. The model is obtained as the extension of [15] by including higher derivative terms (O(R4 )) in the eleven dimensional supergravity action. We studied the following issues in the context of holographic thermal QCD at intermediate coupling.

• Deconfinement Phase Transition in Thermal QCD-Like Theories at Intermediate Coupling: We discussed the deconfinement phase transition in thermal QCD from the semi-classical method and entanglement entropy point of view. The semi-classical method is based on the Hawking Page phase transition between thermal and black hole background on the gravity dual side. The procedure is to obtain the on-shell action densities of thermal and black hole backgrounds and equates these two at the UV cut-off. We obtained the deconfinement temperature of thermal QCD by equating the leading order terms. We observed the “UV-IR” mixing, “Flavor Memory” effect, and “non-renormalization of Tc”. Let us explain these effects in some detail.

UV-IR Mixing and Flavor Memory Effect: When we equated the on-shell action densities at the UV cut-off, then we obtained a relationship between the integration constants appearing in the black hole background along the compact part of the noncompact four cycle, which is part of the flavor D7-branes worldvolume and higher derivative correction to the thermal background along the M-theory circle. This is called “UV-IR mixing” in our setup. Since the aforementioned integration constants are associated with the flavor D7-branes of parent type IIB string dual and hence they have the information about the flavor branes in the M-theory uplift, which has no branes. This is interpreted as the “Flavor Memory” effect in our setup.

Non-Renormalization of Tc: The deconfinement phase transition in thermal QCD corresponds to phase transitions between the entanglement entropies of connected and disconnected surfaces in the language of gauge-gravity duality. We showed that the deconfinement phase transition occurs at the critical value of the length of the interval chosen to compute the entanglement entropy. In this process, we found that entanglement entropies of connected and disconnected surfaces do not receive the O(R4 ) corrections, and hence Tc does not receive the same. This is known as the non-renormalization of the deconfinement temperature of thermal QCD-like theories.

MχPT-Tc Compatibility: While matching one of the one-loop renormalized LECs with the phenomenological data in [2], we imposed the constraint on the combination of integration constants mentioned earlier but now for the thermal background. The constraint was that one would get the exact matching with phenomenological data provided the combination, as mentioned above, should have a negative sign. In this paper, we explicitly calculated the expressions of integration constants for the thermal background and showed that the constraint is satisfied, and hence we showed the compatibility between our chiral perturbation theory study and deconfinement temperature computation.

• Deconfinement Phase Transition in Rotating QGP at Intermediate Coupling: We constructed the holographic dual of rotating QGP by making one of the spatial coordinates in the M-theory dual periodic and performing the Lorentz transformation along the temporal and the periodic coordinate mentioned earlier. The gravity dual will be a rotating cylindrical black hole and thermal backgrounds when T > Tc and T < Tc on the thermal QCD side. Since the cylindrical black hole has the angular velocity, this maps to the angular velocity of rotation of QGP in thermal QCD via gauge-gravity duality. We followed the semi-classical method to study the deconfinement phase transition in rotating QGP from a top-down model. We found that the deconfinement temperature of thermal QCD is inversely proportional to the Lorentz factor, implying that as QGP rotation increases, Tc decreases and vice-versa. When we analyze the effect of higher derivative terms similar to [3], we found that one again observed “UV-IR mixing”, “Flavor Memory effect”, and “non-renormalization of Tc” even in the rotating QGP. In this paper, we showed the normalization of Tc by calculating the higher derivative correction to the Hawking temperature too. Since, Hawking temperature maps to Tc on the QCD side via Hawking-Page phase transition in the context of gauge-gravity duality. We found that Hawking temperature receives no higher derivative corrections, guaranteeing that Tc is non-renormalized.

Future Physics outlook:

• The LEC H1 of (2.1) and, in general, the LECs of the χPT Lagrangian at O(p 6 ) [124] may be calculated using the given values of the parameters of our M-theory dual of thermal QCD-like theories.