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by Multiverse Theory: as real as the movies make it out to beFebruary 22nd, 2024

**Authors:**

(1) Gopal Yadav, Department of Physics, Indian Institute of Technology & Chennai Mathematical Institute.

**PART I**

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

Chapter 4: Conclusion and Future Outlook

**PART II**

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

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

Chapter 9: Multiverse in Karch-Randall Braneworld

Chapter 10: Conclusion and Future outlook

This chapter is based on the paper [2]. Some portion of [2] is already present in a thesis of one of the co-authors (VY) [83]. Detailed calculations of the relevant quantities appearing in this chapter are given in [83]. Hence, we will quote those results in appendix A without going into the details and use those results to calculate the low energy coupling constants (LECs) of SU(3) chiral perturbation theory in the chiral limit.

Holographic computation of SU(3) LECs was done in [84] from the top-down Sakai-Sugimoto model [90]. The Sakai-Sugimoto model is not UV complete. The Lagrangian obtained in [84] is different from the SU(3) χPT Lagrangian given in [87]. The paper [91] contains the relationship between the SU(3) LECs and the coupling constants obtained in [84]. We obtained these LECs from a UV complete top-down holographic dual. The gravity dual is type IIA string theory in the presence of higher derivative terms. Type IIA background had been obtained by descending back from the M-theory to type IIA string theory.

The term appearing in the SU(3) χPT Lagrangian at O(p 4 ) with one-loop renormalized low energy constants (LECs),Li and Hi , in chiral limit are written as follows [87]:

The divergent piece, λ(µ) appearing in (2.2) is given below.

where d = 4. The phenomenological values of the one-loop renormalized SU(3) LECs appearing in (2.1) are listed in the table 2.1 [89]. In table 2.2 sources from where the LECs have been extracted is given for the column titled GL 1985 [87]. In the chiral perturbation

theory that is used in gauge-gravity duality, the holographic renormalization acts as the analogue of the one-loop renormalization. The eleven dimensional on-shell supergravity action including O(β) correction was worked out in [3] and written below:

The simplified expressions of the radial integrals appearing in (2.18) are given in the appendix A. Relation between SU(3) LECs of [87] (equation (2.1)) and couplings appearing from holographic computation (equation (2.15)) was obtained in [91]:

In this chapter, we computed the LECs of SU(3) chiral perturbation theory from the type IIA string dual inclusive of O(R4 ) corrections. We constructed the SU(3) Lagrangian and obtained the coupling constants from the radial integrals quoted in appendix A. We already mention in the beginning of this chapter that we have used the results of [2, 83] to do our calculations in this chapter. My contribution has been presented in this chapter.

All the above points are summarised in the table 2.3.

This paper is available on arxiv under CC 4.0 license.

L O A D I N G

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