arXiv subjects

Sitender Pratap Kashyap

Publications and source records attributed to Sitender Pratap Kashyap.

17 recordsLinked to original sources

arXiv2026

A field-inspired derivation of open string amplitudes

We propose a new method for computing $N$-point tree-level open string amplitudes, inspired by the field-theoretical perturbiner framework and bypassing world-sheet moduli integration. The construction rests on a weak associativity condition for a point-split, on-shell product of string vertices, introducing a binary-tree prescription with all physical channels manifest. The output is a multi-parametric series representation of the partial amplitude that is amenable to mass-level truncation and, therefore, numerical implementation. Besides the Veneziano amplitude, automatically represented by a dual-channel series with one free parameter, we present its five-point generalization, involving two free parameters and matched against known results in the literature. Higher multiplicities are obtained via the same systematic branching, with no separate input.

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arXiv2025

Two point amplitude for closed superstrings

We present a prescription for computing the tree-level two-point amplitude of closed strings in the pure spinor superstring formalism, thereby completing the analysis of such superstring amplitudes. The construction relies on fixing the residual conformal Killing group using a mostly BRST-exact operator that has been successfully applied in the open-string case. Earlier attempts at a straightforward extension to closed strings--treating them naïvely as products of open strings--fail. Nevertheless, we show that a consistent prescription can be obtained by replacing the open-string BRST charge with the closed-string BRST charge. The key idea is to employ closed-string vertex operators with nonstandard ghost-number assignments, rather than the conventional ghost-number (1,1) vertices. Furthermore, since the pure spinor BRST cohomology for closed strings vanishes at total (left plus right) ghost number four or higher, we find that the resulting prescription is essentially unique.

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arXiv2025

Tension between string amplitude prescriptions with presumed spacetime supersymmetry

We analyze an alternative prescription for computing tree level scattering amplitudes in the pure spinor superstring. Proposed by Berkovits, and inspired by an earlier work by Lee and Siegel, it bypasses the traditional ghost number three measure of the pure spinor ghosts, $\langleλ^3 θ^5\rangle$=1, arguably simplifying the calculation. However, direct computations using the free field OPEs of the target superspace CFT fail to reproduce the expected $\textrm{SL}(2,\mathbb{C})$ invariance of tree level correlators. This persistent mismatch, confirmed through independent methods, is not compatible with the gauge invariance of the amplitude. We also discuss possible implications for the B-RNS-GSS formalism of the superstring.

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arXiv2025

Massless representation of massive superfields and tree amplitudes with the pure spinor formalism

We construct the unintegrated vertex operator at the first mass level of the open superstring from the OPE of massless vertices. Using BRST cohomology manipulations, the tree amplitude of two massless and one massive state is rewritten in terms of the pure spinor superspace kinematic expression of the massless four-point amplitude at the ${α^\prime}^2$ level. A generalization relating the partial $n$-point tree amplitudes with one massive state and linear combinations of the ${α^\prime}^2$ corrections to n+1 massless amplitudes is found and shown to be consistent with unitarity.

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arXiv2024

de Sitter Teukolsky waves

We present de Sitter Teukolsky waves -- linearised quadrupolar gravitational waves in the transverse-traceless gauge in de Sitter spacetime. In the cosmological constant $Λ$ going to zero limit, our solutions match to Teukolsky solutions. For non-zero $Λ$, we compare our solutions to the wider literature, where different authors have constructed linearised gravitational perturbations in de Sitter spacetime with varied motivations. For de Sitter Teukolsky waves, we compute the energy flux across future timelike infinity $\mathcal{I}^{+}$ and show that it is manifestly positive.

gr-qc↗

arXiv2023

A relation between massive and massless string tree amplitudes

We uncover a relation between the scattering amplitudes of massive strings and the $α'$ expansion of the massless string amplitude at tree level. More precisely, the n-point tree amplitude of n-1 massless and one massive state is written as a linear combination of n+1 massless string amplitudes at the $α'^2$ order.

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arXiv2023

Two-Point Superstring Tree Amplitudes Using the Pure Spinor Formalism

We provide a prescription for computing two-point tree amplitudes in the pure spinor formalism that are finite and agree with the corresponding expression in the field theories. In [arXiv:1906.06051v1-arXiv:1909.03672v3], same results were presented for bosonic strings and it was mentioned they can be generalized to superstrings. The pure spinor formalism is a successful super-Poincare covariant approach to quantization of superstrings [arXiv:hep-th/0001035v2]. Because the pure spinor formalism is equivalent to other superstring formalisms, we explicitly verify the above claim. We introduce a mostly BRST exact operator in order to achieve this.

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arXiv2023

Theory dependence of black hole interior reconstruction and the extended strong subadditivity

An AdS eternal black hole in equilibrium with a finite temperature bath presents a Hawking-like information paradox due to a continuous exchange of radiation with the bath. The non-perturbative gravitational effect, the replica wormhole, cures this paradox by introducing a non-trivial entanglement wedge for the bath after Page time. In this paper, we analyse the theory dependence of this non-perturbative effect by randomising the boundary conditions of some of the bulk matter fields. We explicitly analyse this in JT gravity by introducing a matter CFT in the AdS region with random boundary conditions at the AdS boundary that are drawn from a distribution. Using the island formula and the extended strong subadditivity due to Carlen and Lieb, we show that at late times the black hole interior is contained inside the entanglement wedge of a reference Hilbert space that encodes the information about the random boundary conditions. Consequently, the reconstruction of the black hole interior from the radiation, in particular the region near the singularity, requires a detailed knowledge of the theory.

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arXiv2023

One Loop Mass Renormalization of Massive States Using Pure Spinor Formalism

As a check of the first massive integrated vertex operator in the pure spinor formalism constructed in arXiv:1802.04486, we compute the one loop 2-point function of the stable non-BPS massive states in SO(32) heterotic string theory. This allows us to compute the one loop renormalized mass of these states using the pure spinor formalism. Our results are in agreement with the corresponding results obtained by Sen using the RNS formalism. This provides an instance of the equivalence between the RNS and the pure spinor formalism for the massive states at loop level.

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arXiv2022

The Mostly BRST Exact Operator in Superstrings

A careful gauge fixing of the conformal killing group (CKG) on genus zero surfaces in bosonic string theory gives non-vanishing two point amplitudes that match the corresponding field theory expressions arXiv:1906.06051, arXiv:1909.03672 . An important ingredient for gauge fixing two point amplitudes in arXiv:1909.03672 was the mostly BRST (mBRST) exact operator. The utility of this operator in gauge fixing CKG perhaps is not just limited to two point amplitudes - we can insert a mBRST exact operator to fix a conformal killing vector (CKV) instead of fixing the position of a vertex operator in a general tree level bosonic string amplitude arXiv:2108.05628, arXiv:2109.08433. Using the mBRST exact operator, written in the pure spinor variables, we get the expected two point superstring amplitudes arXiv:2012.03802. In this work we explore if it is possible to use this operator for fixing CKG for general tree level amplitudes in superstrings. We find it to be the case by explicitly re-calculating the three gluon amplitude in open strings by making use of this operator. Finally, we show that this operator directly emerges by following a Faddeev-Popov gauge fixing method in bosonic string theory. This derivation is independent of the number of external strings, thus proving the above claim.

hep-th↗

arXiv2018

Integrated Massive Vertex Operator in Pure Spinor Formalism

We construct the integrated vertex operator for the first massive states of open superstrings with $(mass)^2=1/α'$ in the pure spinor formalism of the superstring theory. This vertex operator is expressed in terms of the ten dimensional $\mathcal{N}=1$ superfields describing the massive supermultiplet which appear in the unintegrated vertex operator of the same states.

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arXiv2018

Amplitudes Involving Massive States Using Pure Spinor Formalism

Same amplitudes evaluated independently using RNS and pure spinor formalism are expected to agree. While for massless states, this fact has been firmly established, for massive states such an explicit check has been lacking so far. We compute all massless-massless-massive 3-point functions in open supertrings in pure spinor formalism for the first massive states and compare them with the corresponding RNS results. We fix the normalization of the vertex operators of the massive states by comparing same set of 3-point functions for a fixed ordering in the two formalisms. Once fixed, the subsequent 3-point functions for each inequivalent ordering match exactly. This extends the explicit demonstration of equivalence of pure spinor and RNS formalism from massless states to first massive states.

hep-th↗

arXiv2017

Testing Subleading Multiple Soft Graviton Theorem for CHY Prescription

In arXiv:1707.06803 we derived the subleading multiple soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. In this paper we verify this explicitly using the CHY formula for tree level scattering amplitudes of arbitrary number of gravitons in Einstein gravity. We pay special care to fix the signs of the amplitudes and resolve an apparent discrepancy between our general results in arXiv:1707.06803 and previous results on soft graviton theorem from CHY formula.

hep-th↗

arXiv2017

Subleading Soft Theorem for Multiple Soft Gravitons

We derive the subleading soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. Our results are valid to all orders in perturbation theory when the number of non-compact space-time dimensions is six or more, but only for tree amplitudes for five or less non-compact space-time dimensions due to enhanced contribution to loop amplitudes from the infrared region.

hep-th↗

arXiv2017

Closed Superstring Field Theory and its Applications

We review recent developments in the construction of heterotic and type II string field theories and their various applications. These include systematic procedures for determining the shifts in the vacuum expectation values of fields under quantum corrections, computing renormalized masses and S-matrix of the theory around the shifted vacuum and a proof of unitarity of the S-matrix. The S-matrix computed this way is free from all divergences when there are more than 4 non-compact space-time dimensions, but suffers from the usual infrared divergences when the number of non-compact space-time dimensions is 4 or less.

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arXiv2017

Theta Expansion of First Massive Vertex Operator in Pure Spinor

We provide the covariant superspace equations that are sufficient to determine the complete $θ$ expansion of the vertex operator of the open string massive states with $(mass)^2=1/α'$ in pure spinor formalism of superstring theory. These equations get rid of the redundant degrees of freedom in superfields and are consistent with the BRST conditions derived in [1]. Further, we give the explicit $θ$ expansion of the superfields appearing in the unintegrated vertex to $O(θ^3)$. Finally, we compute the contribution to a 3-point tree amplitude with the resulting vertex operator upto $O(θ^3)$ and find its kinematic structure to be identical to the corresponding RNS computation.

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arXiv2015

Surviving in a Metastable de Sitter Space-Time

In a metastable de Sitter space any object has a finite life expectancy beyond which it undergoes vacuum decay. However, by spreading into different parts of the universe which will fall out of causal contact of each other in future, a civilization can increase its collective life expectancy, defined as the average time after which the last settlement disappears due to vacuum decay. We study in detail the collective life expectancy of two comoving objects in de Sitter space as a function of the initial separation, the horizon radius and the vacuum decay rate. We find that even with a modest initial separation, the collective life expectancy can reach a value close to the maximum possible value of 1.5 times that of the individual object if the decay rate is less than 1% of the expansion rate. Our analysis can be generalized to any number of objects, general trajectories not necessarily at rest in the comoving coordinates and general FRW space-time. As part of our analysis we find that in the current state of the universe dominated by matter and cosmological constant, the vacuum decay rate is increasing as a function of time due to accelerated expansion of the volume of the past light cone. Present decay rate is about 3.7 times larger than the average decay rate in the past and the final decay rate in the cosmological constant dominated epoch will be about 56 times larger than the average decay rate in the past. This considerably weakens the lower bound on the half-life of our universe based on its current age.

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