Investigations of LST and WCFT using complexity as a probe

Katoch, Gaurav (2023) Investigations of LST and WCFT using complexity as a probe. PhD thesis, Indian Institute of Technology, Hyderabad.

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AdS/CFT, or more broadly speaking gauge/gravity duality has revolutionized our understanding of strongly coupled quantum field theories. For a large class of field theories, calculations which were once considered beyond reach due to the breakdown of coupling constant perturbation theory are now routinely being done by first mapping the field theory to its gravity dual (often constructed from the “bottom-up” without even the need for knowledge of any details of string the- ory), and then solving (numerically in most cases) the classical gravity-matter system, i.e. Ein- stein field equations coupled to classical matter fields. This so-called “holographic approach” of solving strongly coupled (gauge) field theories has extended the use of gravitational methods(GR/SUGRA) to the fields of condensed matter physics. and QCD. However, the impact of AdS/CFT (gauge/gravity) has been far more deep and revealing than merely providing a classical geometrical computational tool for strongly coupled field theory phe- nomena. Thinking about how field theory codes various phenomena on the gravity side, such as emergence of a quasilocal bulk spacetime local observables propagating on it, spatial connectivity of the bulk geometry, event horizons and gravitational singularities etc., has led to the recognition and importance of various concepts from the quantum information and computation (QIC) litera- ture which capture aspects of quantum field theories not captured by traditional observables such as correlation functions of local operators or Wilson loops. Information geometry/information metrics, Von-Neumann and Renyi Entropy, Mutual Information, Tensor networks Computational Complexity, Fidelity susceptibility, Quantum error correcting codes are only to name a few. This has become a highly productive enterprise leading to insights that might even solve the information paradox. Combining insights from holographic gravity duals, from integrability or super- symmetry-based arguments, from lattice-based approaches and perturbative approaches, we have explored the landscape of local quantum field theories rather comprehensively. Chapter 1 of this thesis gives a short review of AdS/CFT correspondence as to how it arises together with its im- portant ingredients viz. AdS background and the boundary conformal field theory. In this thesis we employ the notion of holographic complexity to navigate the lesser chartered ter- ritories like timelike singularities, non-local and lorentz violating field theories and warped CFT’s. In places we have leveraged the holographic tools to define the boundary gauge theory using the bulk description. thereby studied the characteristics of the boundary gauge theory by quantifying their complexity. The complexity is defined holographically by Susskind’s complexity volume and complexity action conjectures. Both of the conjectures of CV and CA as they came to be known, comes handy when characterizing the universal features of quantum complexity of the boundary field theory. Quantum complexity has emerged to be a crucial property of field theories capable of capturing physical phenomena which cannot be easily captured by more traditional field the- ory probes such as correlation function of local operators, and is touted to play a major role in holographic bulk reconstruction. We also compare and contrast the outcomes of both prescrip- tions to the extent that they appear as a viable tool in capturing the formerly obscure content of boundary field theory. In chapter 2 of the thesis, we introduce the notion of holographic quantum complexity and present the reasoning for its introduction as a viable tool. Combining insights from complementary approaches such as holography, integrability or super- symmetry based arguments, lattice based approaches and perturbative approaches, we have ex- plored the landscape of local quantum field theories rather comprehensively. However, the land- scape of nonlocal quantum field theories is still mostly unexplored. We are optimistic that holog- raphy will be as productive in demystifying properties of nonlocal quantum field theories such as the LST as it has been for enhancing our understanding of strongly coupled regimes of local field theories. Another fact is that holography beyond the traditional asymptotically AdS setting is also little explored. Our hope is that studying set ups such as the LST will help us get an handle on nonperturbative quantum gravity beyond pure AdS asymptotics to flat asymptotics. In chapter 3 we present the study of string theory in the background that interpolates between AdS3 in the IR to flat spacetime with a linear dilaton in the UV. The boundary dual theory in- terpolates between a CFT2 in the IR to a certain two-dimensional Little String Theory (LST) in the UV. In particular, we study computational complexity of such a theory through the lens of holography and investigate the signature of non-locality in the short distance behavior of com- plexity. When the cutoff UV scale is much smaller than the non-locality (Hagedorn) scale, we find exotic quadratic and logarithmic divergences (for both volume and action complexity) which are not expected in a local quantum field theory. We also generalize our computation to include the effects of finite temperature. Up to second order in finite temperature correction, we do not any find newer exotic UV-divergences compared to the zero temperature case. Thereafter, chapter 4 is the generalization of our work presented in previous chapter where we exploited holography to compute the complexity characteristics of Little String Theory (LST), a nonlocal, non-gravitational field theory which is connected via RG flow to local 2d CFT in the IR by an integrable irrelevant (TT) deformation. In this work, we look at the LST obtained by fur- ther deforming the 2d CFT by Lorentz violating irrelevant JT and TJ deformations, in an effort to capture the novel signatures of Lorentz violation (on top of nonlocality) on quantum complex- ity. It turns out that for this system the nonlocality and Lorentz violation effects are inextricably intertwined in the divergence structure of the quantum complexity. In anticipation of the fact that the dual field theory is lorentz violating, we compute the volume complexity in two different lorentz frames and the comparison is drawn between the results. These new results are consistent with our previous work, and null warped AdS3 is treated as special case of interest. In chapter 5 we investigate WCFT2 s using circuit complexity as a tool. Warped conformal field theories in two dimensions are exotic nonlocal, Lorentz violating field theories characterized by Virasoro-Kac-Moody symmetries and have attracted a lot of attention as candidate boundary du- als to warped AdS3 spacetimes, thereby expanding the scope of holography beyond asymptoti- cally AdS spacetimes. First we compute the holographic volume complexity (CV) which displays a linear UV divergence structure, more akin to that of a local CFT2 and has a very complicated dependence on the Virasoro central charge c and the U(1) Kac-Moody level parameter k. Next we consider circuit complexity based on Virasoro-Kac-Moody symmetry gates where the com- plexity functional is the geometric (group) action on coadjoint orbits of the Virasoro-Kac-Moody group. We consider a special solution to extremization equations for which complexity scales lin- early with “time”. In the semiclassical limit (large c, k, while c/k remains finite and small) both the holographic volume complexity and circuit complexity scales with k. In the final chapter 6, we turn our attention towards the quantum complexity of CFT/quantum gravity states which are dual to bulk geometries containing a naked timelike singularity. The ap- pearance of naked timelike singularities in semiclassical limit are allowed in string theory, par- ticularly in the context of holography, so long as they satisfy the “Gubser criterion” - only those naked timelike singularities are admissible which arise in the extremal limits of geometries con- taining cloaked singularities. In this work, we formulate an analogous criterion for the appearance of naked timelike singularities based on holographic complexity. We study three specific cases of naked timelike singularities, namely the negative mass Schwarzschild-AdS spacetime, the timelike Kasner-AdS and Einstein-dilaton system. The first two cases are outright ruled out by the Gub- ser criterion while the third case is more subtle - according to the Gubser criterion the singularity switches from forbidden to admissible as the parameter δ is dialed in the range [0, 1] across the transition point at δ = 1/ √ 3. We probe all three geometries using two holographic complexity prescriptions, namely CA and CV. We propose a simple criterion that if the holographic complex- ity of a geometry with naked timelike singularities is less than that of empty AdS, then that sin- gularity cannot arise in the semiclassical limit of a UV-complete theory of quantum gravity. Our study strongly suggests that action complexity (CA) is a sensitive tool to investigate of timelike singularities being perfectly consistent with the Gubser criterion in all cases. On the other hand, volume complexity (CV) turns out to be not a reliable tool to probe timelike singularities.

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IITH Creators:
IITH CreatorsORCiD
Item Type: Thesis (PhD)
Uncontrolled Keywords: CFD; LST; WCFT; Renyi Entropy, WCFT; Gubser criterion; gauge; gravity; Von-Neumann; Renyi Entropy, Mutual Information,Tensor networks, Computational Complexity, Fidelity, susceptibility,
Subjects: Physics
Physics > Modern physics
Divisions: Department of Physics
Depositing User: Mr Nigam Prasad Bisoyi
Date Deposited: 17 Aug 2023 10:18
Last Modified: 28 Aug 2023 11:41
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