arXiv subjects

Gaurav Narain

Publications and source records attributed to Gaurav Narain.

At least 19 recordsLinked to original sources

arXiv2026

Boundary conditions for axionic wormholes, imaginary distance bound and KSW allowability

We study four-dimensional axion wormholes in the Lorentzian mini-superspace path integral using dual scalar and three-form flux formulations. We analyze this duality for generic metric boundary conditions and real lapse integration contour, and show that it holds on any background, including complex ones. With the Dirichlet condition on the metric, the fixed-flux path integral is evaluated exactly. In the Euclidean regime, saddle geometries organize into same-side and cross-throat segments of the Giddings-Strominger (GS) wormhole, depending on whether the two boundaries lie on the same or opposite sides of the throat. A Picard-Lefschetz analysis in the covering plane of lapse reveals that the cross-throat saddle has vanishing intersection number, and therefore does not contribute. In the asymptotically flat limit, it corresponds to the imaginary wormhole that saturates the imaginary distance bound (IDB). The same conclusion follows independently on the scalar side of the duality, and is confirmed by the exact amplitude. Replacing the Dirichlet condition with a one-parameter Neumann condition, the cross-throat saddle that leads to the imaginary wormholes remains irrelevant for the physical lift of the contour. This purely imaginary parameter characterizing the Neumann condition interpolates continuously between the half- and complete-wormhole geometries. Convergence of the sum over fixed-charge sectors imposes a corresponding interpolating bound not only on the imaginary part of the boundary axion but also on the parameter characterizing the Neumann boundary condition. An independent analysis based on the KSW criterion reproduces exactly the same bound, emphasizing its compatibility with the IDB.

hep-th↗

arXiv2026

IR behaviour of one-loop complex $\mathbb{R}\times S^3$ saddles

Gravitational path-integral over $\mathbb{R}\times S^3$ complex metrics with fluctuations is studied in 4D for Einstein-Hilbert gravity in Lorentzian signature, with the aim to investigate the IR properties of complex saddles for various boundary choices. General covariance doesn't allow arbitrary boundary choices for the background and fluctuations. In the ADM-decomposition, while imposing ``no-boundary'' condition at the initial boundary, two scenarios are considered for the final boundary: Dirichlet and fixed extrinsic curvature. Universe undergoes transition from a Euclidean to Lorentzian phase in either scenario, where the dominant saddle in Euclidean phase correspond to a Euclidean metric (imaginary time), while the Lorentzian phase has two complex metrics as dominant saddles which superimpose. One-loop corrected lapse action is computed using Hurwitz-Zeta regularization. UV-divergences canceled by suitable counter terms lead to a renormalized lapse action. One-loop renormalized Hartle-Hawking wave-function is computed using the Picard-Lefschetz and WKB methods, where the contributions coming from the metric-fluctuations show secularly growing infrared divergences as the Universe expands. This is compared with the situation in pure Lorentzian dS, corresponding to a Universe transitioning from an initial state of vanishing conjugate momenta to final state of fixed extrinsic curvature, thereby giving real saddles. Picard-Lefschetz methods alone are not sufficient to overcome the technical hurdles in the one-loop computation, which needs to be supplemented by an $i\epsilon$-prescription, achieved via slight complexification of the cosmological constant $\Lambda$. The UV renormalized one-loop dS wavefunction has the same leading IR divergence as for the Hartle-Hawking no-boundary Universe. Interestingly for all boundary choices considered, the saddles remain KSW-allowed.

hep-th↗

arXiv2026

Note on KSW-allowability of Wine-Glass Geometry

In this note we consider no-boundary instantons and wine-glass geometries which are of interest in the context of quantum cosmology. While the former usually appears as a dominant saddle in the path-integral, the wineglass geometry can become dominant saddle in some situations. The later has been argued to have a longer inflationary phase of the Universe. Kontsevich-Segal-Witten (KSW)-allowability criterion which classifies geometries on the basis of the requirement of having a meaningful QFT on it, pushes one to analyse the allowability of the various geometries. In this note we do a simple study to seek answer to the allowabilty of no-boundary instantons and wine-glass geometries, where the later is obtained via analytical continuation of Lorentzian deSitter in pure gravity. Our simple analysis which make use of a milder version of KSW allowability criterion shows that no-boundary instanton is KSW allowed while wine-glass geometries obtained via such analytic continuation in pure-gravity are KSW disallowed. This study however doesn't covers wineglass saddles arising in gravity coupled with matter theories.

hep-th↗

arXiv2025

RG studies of scalar-field models of long-range interactions

In this work we studies the long-range interactions in non-gravitational field theories and their behaviour in the deep infrared. To model such effects, we consider a nonlocal scalar theory obtained by adding a $\phi\Box^{-1}\phi$ term to the local action. Using the functional renormalisation group, we analyse its infrared fixed-point structure. Within the LPA, we show that nonlocality modifies phase-transition patterns and can induce symmetry breaking. Extending the LPA beyond polynomial truncations, we examine the convexity property of the effective potential as $k\rightarrow 0$ and find that the flow becomes singular for $\lambda^{2}>0$ before reaching the deep infrared. In the LPA$'$ framework, we find that the infrared-stable fixed point is the nonlocal Gaussian fixed point. We then generalise the model to $\phi\Box^{\sigma/2}\phi$ and analyse how the infrared properties depend on $\sigma$. With appropriate scaling choices, we show that the infrared behaviour remains unchanged up to $\sigma=d/2$ and follows Sak's prediction up to $\sigma=2$. Finally, we study higher-derivative cases within the LPA, focusing on $\sigma=4$, which corresponds to isotropic Lifshitz criticality, and obtain results consistent with earlier work.

hep-th↗

arXiv2025

Complex Saddles of Charged-AdS Gravitational partition function

In this paper, we consider the Euclidean partition function of uncharged and charged $AdS_{d+1}$ black hole geometries in canonical and grand canonical ensemble for $d\geq3$. It is seen that the partition function can be reduced to a one-dimensional integral, which can be investigated using methods of Picard-Lefschetz. The saddles of the system correspond to either naked-singular geometry, thermal-AdS, small-, intermediate- or large-sized black hole for different ranges of parameter space. These are solutions of Einstein's equation, which are dominant saddles of the partition function in various regimes of parameter space. A naive analysis of the partition function involving these saddles would lead to conflicts with the standard understanding of black hole thermodynamics and also with AdS/CFT. However, when the partition function is analysed using Picard-Lefschetz, it is seen that naked-singular geometries turn out to be irrelevant and therefore do not contribute. This also aligns well with the Cosmic Censorship hypothesis. Depending on the ensemble, saddles corresponding to negative specific heat are either small- or intermediate-sized black holes. Although they are relevant in the partition function but are sub-dominant. They drop out under homology averaging. Only saddles corresponding to non-negative specific heat contribute to the Euclidean partition function. Finally, we analyze the allowability of these complex geometries using the KSW criterion.

hep-th↗

arXiv2025

Resolving Degeneracies in Complex $\mathbb{R}\times S^3$ and $\theta$-KSW

Lorentzian gravitational path integral for the Gauss-Bonnet gravity in $4D$ is studied in the mini-superspace ansatz for metric. The gauge-fixed path-integral for Robin boundary choice is computed exactly using {\it Airy}-functions, where the dominant contribution comes from No-boundary geometries. The lapse integral is further analysed using saddle-point methods to compare with exact results. Picard-Lefschetz methods are utilized to find the {\it relevant} complex saddles and deformed contour of integration, thereby using WKB methods to compute the integral along the deformed contour in the saddle-point approximation. However, their successful application is possible only when system is devoid of degeneracies, which in present case appear in two types: {\bf type-1} where the flow-lines starting from neighbouring saddles overlap leading to ambiguities in deciding the {\it relevance} of saddles, {\bf type-2} where saddles merge for specific choices of boundary parameters leading to failure of WKB. Overcoming degeneracies using artificial {\it defects} introduces ambiguities due to the choice of {\it defects} involved. Corrections from quantum fluctuations of scale-factor overcome degeneracies only partially (lifts {\bf type-2} completely with partial resolution of {\bf type-1}), with the residual lifted fluently by complex deformation of $(G\hbar)$. {\it Anti-linear} symmetry present in various forms in the lapse action is the reason behind all the {\bf type-1} degeneracies. Any form of {\it defect} or {\it deformation} breaking anti-linearity resolves {\bf type-1} degeneracies, indicating complex deformation of $(G\hbar)$ as an ideal choice. Compatibility with the KSW criterion is analyzed after symmetry breaking. Complex deformation of $(G\hbar)$ modifies the KSW criterion, imposing a strong constraint on the deformation if No-boundary geometries are required to be always KSW-allowed.

hep-th↗

arXiv2024

Boundary choices and one-loop complex gravitational path integral

The path integral of 4D Einstein-Hilbert gravity for the de Sitter-like Universe with fluctuations is investigated, and the transition amplitude from one boundary configuration to another is computed. The gravitational system is described by lapse, scale factor and metric-fluctuation field. Variational consistency demands augmenting the bulk theory with suitable boundary action. A given boundary choice on scale factor is seen to be achievable via an infinite family of covariant boundary actions, each restricting the boundary choices for the fluctuation field. General covariance intimately ties the two boundary choices, which no longer can be chosen independently. For vanishing metric fluctuations at the boundaries, the gauge-fixed gravitational path integral disintegrates into path integral over scale factor and metric-fluctuation field, connected via only lapse integration. While the former is exactly doable, the latter is computed up to one loop, leading to one-loop corrected lapse action. Ultraviolet (UV) divergences are systematically extracted and removed by the addition of suitable counterterms, leading to finite effective action for the lapse. The lapse effective action is then utilized for computing finite transition amplitude. Contributions from virtual gravitons are seen to be secularly growing with Universe size, leading to an infrared divergent transition amplitude. The presence of nonvanishing metric fluctuation at the boundaries implies that the ``no-boundary'' saddles of the theory without metric fluctuations are no longer the saddles of the one-loop corrected action. The corrected saddles have the Universe starting from a nonzero size.

gr-qc↗

arXiv2024

Lorentzian Robin Universe of Gauss-Bonnet Gravity

The gravitational path-integral of Gauss-Bonnet gravity is investigated and the transition from one spacelike boundary configuration to another is analyzed. Of particular interest is the case of Neumann and Robin boundary conditions which is known to lead to a stable Universe in Einstein-Hilbert gravity in four spacetime dimensions. After setting up the variational problem and computing the necessary boundary terms, the transition amplitude is computed \emph{exactly} in the mini-superspace approximation. The $\hbar\to0$ limit brings out the dominant pieces in the path-integral which is traced to an initial configuration corresponding to Hartle-Hawking no-boundary Universe. A deeper study involving Picard-Lefschetz methods not only allow us to find the integration contour along which the path integral becomes convergent but also aids in understanding the crossover from Euclidean to Lorentzian signature. Saddle analysis further highlights the boundary configurations giving dominant contribution to the path-integral which is seen to be those corresponding to Hartle-Hawking no-boundary proposal and agrees with the exact computation. To ensure completeness, a comparison with the results from Wheeler-DeWitt equation is done.

gr-qc↗

arXiv2024

Lorentzian Robin Universe

In this paper, we delve into the gravitational path integral of Gauss-Bonnet gravity in four spacetime dimensions, in the mini-superspace approximation. Our primary focus lies in investigating the transition amplitude between distinct boundary configurations. Of particular interest is the case of Robin boundary conditions, known to lead to a stable Universe in Einstein-Hilbert gravity, alongside Neumann boundary conditions. To ensure a consistent variational problem, we supplement the bulk action with suitable surface terms. This study leads us to compute the necessary surface terms required for Gauss-Bonnet gravity with the Robin boundary condition, which wasn't known earlier. Thereafter, we perform an exact computation of the transition amplitude. Through $\hbar\to0$ analysis, we discover that the Gauss-Bonnet gravity inherently favors the initial configuration, aligning with the Hartle-Hawking no-boundary proposal. Remarkably, as the Universe expands, it undergoes a transition from the Euclidean (imaginary time) to the Lorentzian signature (real time). To further reinforce our findings, we employ a saddle point analysis utilizing the Picard-Lefschetz methods. The saddle point analysis allows us to find the initial configurations which lead to Hartle-Hawking no-boundary Universe that agrees with the exact computations. Our study concludes that for positive Gauss-Bonnet coupling, initial configurations corresponding to the Hartle-Hawking no-boundary Universe gives dominant contribution in the gravitational path-integral.

gr-qc↗

arXiv2022

Surprises in Lorentzian path-integral of Gauss-Bonnet gravity

In this paper we study the Lorentzian path-integral of Gauss-Bonnet gravity in the mini-superspace approximation in four spacetime dimensions and investigate the transition amplitude from one configuration to another. Past studies motivate us on imposing Neumann boundary conditions on initial boundary as they lead to stable behaviour of fluctuations. The transition amplitude is computed exactly while incorporating the non-trivial contribution coming from the Gauss-Bonnet sector of gravity. A saddle-point analysis involving usage of Picard-Lefschetz methods allow us to gain further insight of the nature of transition amplitude. Small-size Universe is Euclidean in nature which is shown by the exponentially rising wave-function. It reaches a peak after which the wave-function becomes oscillatory indicating an emergence of time and a Lorentzian phase of the Universe. We also notice an interesting hypothetical situation when the wave-function of Universe becomes independent of the initial conditions completely, which happens when cosmological constant and Gauss-Bonnet coupling have a particular relation. This however doesn't imply that the initial momentum is left arbitrary as it needs to be fixed to a particular value which is chosen by demanding regularity of Universe at an initial time and the stability of fluctuations.

gr-qc↗

arXiv2021

On Gauss-bonnet gravity and boundary conditions in Lorentzian path-integral quantization

Recently there has been a surge of interest in studying Lorentzian quantum cosmology using Picard-Lefschetz methods. The present paper aims to explore the Lorentzian path-integral of Gauss-Bonnet gravity in four spacetime dimensions with metric as the field variable. We employ mini-superspace approximation and study the variational problem exploring different boundary conditions. It is seen that for mixed boundary conditions non-trivial effects arise from Gauss-Bonnet sector of gravity leading to additional saddle points for lapse in some case. As an application of this we consider the No-boundary proposal of the Universe with two different settings of boundary conditions, and compute the transition amplitude using Picard-Lefschetz formalism. In first case the transition amplitude is a superposition of a Lorentzian and a Euclidean geometrical configuration leading to interference incorporating non-perturbative effects coming from Gauss-Bonnet sector of gravity. In the second case involving complex initial momentum we note that the transition amplitude is an analogue of Hartle-Hawking wave-function with non-perturbative correction coming from Gauss-Bonnet sector of gravity.

gr-qc↗

arXiv2020

Lorentzian quantum cosmology in novel Gauss-Bonnet gravity from Picard-Lefschetz methods

In this paper we study some aspects of classical and quantum cosmology in the novel-Gauss-Bonnet (nGB) gravity in four space-time dimensions. Starting with a generalised Friedmann-Lemaître-Robertson Walker (FLRW) metric respecting homogeneity and isotropicity in arbitrary space-time dimension $D$, we find the action of theory in four spacetime dimension where the limit $D\to4$ is smoothly obtained after an integration by parts. The peculiar rescaling of Gauss-Bonnet coupling by factor of $D-4$ results in a non-trivial contribution to the action. We study the system of equation of motion to first order nGB coupling. We then go on to compute the transition probability from one $3$-geometry to another directly in Lorentzian signature. We make use of combination of WKB approximation and Picard-Lefschetz (PL) theory to achieve our aim. PL theory allows to analyse the path-integral directly in Lorentzian signature without doing Wick rotation. Due to complication caused by non-linear nature of action, we compute the transition amplitude to first order in nGB coupling. We find non-trivial correction coming from the nGB coupling to the transition amplitude, even if the analysis was done perturbatively. We use this result to investigate the case of classical boundary conditions.

gr-qc↗

arXiv2020

Cosmic evolution in novel-Gauss Bonnet Gravity

In this short paper we investigate any non-trivial effect the novel Gauss-Bonnet gravity may give rise in the cosmic evolution of the Universe in four spacetime dimensions. We start by considering a generic Friedmann-Lemaître-Robertson-Walker (FLRW) metric respecting homogeneity and isotropicity in arbitrary space-time dimension $D$. The metric depends on two functions: scale factor and lapse. Plugging this metric in novel Einstein-Gauss-Bonnet (EGB) gravity action, doing an integration by parts and then take the limit of $D\to4$ give us a dynamical action in four spacetime dimensions for scale factor and lapse. The peculiar rescaling of Gauss-Bonnet coupling by factor of $D-4$ results in a non-trivial contribution in the action of the theory. In this paper we study this action. We investigate the dynamics of scale-factor and behavior of lapse in an empty Universe (no matter). Due to complexity of the problem we study the theory to first order in Gauss-Bonnet coupling and solve system of equation to the first order. We compute the first order correction to the on-shell action of the empty Universe and find that its sign is opposite of the leading order part. We discuss it consequences.

gr-qc↗

arXiv2019

Lorentzian quantum cosmology with $R^2$ correction

Quantum mechanical transition amplitudes directly tells the probability of each transition and which one is more favourable. Path-integrals offers a systematic methodology to compute this quantum mechanical process in a consistent manner. Although it is not complicated in simple quantum mechanical system but defining path-integral legitimately becomes highly nontrivial in the context of quantum-gravity, where apart from usual issues of renormalizability, regularisation, measure, gauge-fixing, boundary conditions, one still has to define the sensible integration contour for convergence. Picard-Lefschetz (PL) theory offers a unique way to find a contour of integration based on the analysis of saddle points and the steepest descent/ascent flow lines in the complex plane. In this paper we make use of PL-theory to investigate Lorentzian quantum cosmology where the gravity gets modified in the ultraviolet with the $R^2$ corrections. We approach the problem perturbatively and compute the transition amplitude in the saddle point approximation to first order in higher-derivative coupling. This perturbative approximation is valid in certain regimes but the approximation cannot be used to address issues of very early Universe or no-boundary proposal.

gr-qc↗

arXiv2019

AdS backgrounds and induced gravity

In this paper we look for AdS solutions to generalised gravity theories in the bulk in various spacetime dimensions. The bulk gravity action includes the action of a non-minimally coupled scalar field with gravity, and a higher-derivative action of gravity. The usual Einstein-Hilbert gravity is induced when the scalar acquires a non-zero vacuum expectation value. The equation of motion in the bulk shows scenarios where AdS geometry emerges on-shell. We further obtain the action of the fluctuation fields on the background at quadratic and cubic orders.

hep-th↗

arXiv2019

Non-locality effect on the entanglement entropy in deSitter

We investigate the effect of infrared non-locality on the entanglement between two causally separated open-charts in the deSitter space-time. Inspired by the work of Maldacena and Pimentel who gave a precise methodology for the computation of the long-range entanglement for the local massive scalar field theory on deSitter space-time, we aim to investigate the change in behaviour of this long-range entanglement due to the presence of infrared non-locality in the theory. By considering a nonlocal scalar field theory where the non-locality becomes important in the infrared, we follow the footsteps of Maldacena and Pimentel to compute the entanglement entropy of the free non-local scalar field theory in the Bunch-Davies vacuum. It is found that the presence of infrared non-locality will have strong effect on the long-range entanglement. In some case it is noted that if the strength of non-locality is large then it will tend to decrease the long-range entanglement in the infrared. We also consider the behaviour of Rényi entropy, where a strong role of non-locality on the entropy is noticed.

hep-th↗

arXiv2019

Entanglement entropy of non-local theories in AdS

We investigate the effect of non-locality on entanglement entropy in anti-de Sitter space-time. We compute entanglement entropy of a nonlocal field theory in anti-de Sitter space-time and find several interesting features. We find that area law is followed, but sub-leading terms are affected by non-locality. We also find that the UV finite term is universal. For the massless theory in 3 dimensional AdS we compute it exactly and find the novel feature that it shows oscillatory behavior.

hep-th↗

arXiv2019

Non-local scalar field on deSitter and its infrared behaviour

We investigate free non-local massless and massive scalar field on deSitter (dS) space-time. We compute the propagator for the non-local scalar field for the corresponding theories on flat and deSitter space-times. It is seen that for the non-local theory, the massless limit of massive propagator is smooth for both flat and deSitter. Moreover, this limit matches exactly with the massless propagator of the non-local scalar field for both flat and deSitter space-time. The propagator is seen to respect dS invariance. Furthermore, investigations of the non-local Green's function on deSitter for large time-like separation shows that the propagator has no infrared divergences. The dangerous infrared $\log$-divergent contributions which arise is local massless theories are absent in the corresponding non-local version. Lack of infrared divergences in the propagator hints at the strong role non-localities may play in the dS infrared physics. This study suggest that non-locality can cure IR issues in deSitter.

hep-th↗