arXiv subjects

Renann Lipinski Jusinskas

Publications and source records attributed to Renann Lipinski Jusinskas.

32 records · Page 2Linked to original sources

arXiv2021

Scattering Massive String Resonances through Field-Theory Methods

We present a new method, exact in $α'$, to explicitly compute string tree-level amplitudes involving one massive state and any number of massless ones. This construction relies on the so-called twisted heterotic string, which admits only gauge multiplets, a gravitational multiplet, and a single massive supermultiplet in its spectrum. In this simplified model, we determine the moduli-space integrand of all amplitudes with one massive state using Berends-Giele currents of the gauge multiplet. These integrands are then straightforwardly mapped to gravitational amplitudes in the twisted heterotic string and to the corresponding massive amplitudes of the conventional type-I and type-II superstrings.

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arXiv2021

The $L_{\infty}$ structure of gauge theories with matter

In this work we present an algebraic approach to the dynamics and perturbation theory at tree-level for gauge theories coupled to matter. The field theories we will consider are: Chern-Simons-Matter, Quantum Chromodynamics, and scalar Quantum Chromodynamics. Starting with the construction of the master action in the classical Batalin-Vilkovisky formalism, we will extract the $L_{\infty}$-algebra that allow us to recursively calculate the perturbiner expansion from its minimal model. The Maurer-Cartan action obtained in this procedure will then motivate a generating function for all the tree-level scattering amplitudes. There are two interesting outcomes of this construction: a generator for fully-flavoured amplitudes via a localisation on Dyck words; and closed expressions for fermion and scalar lines attached to $n$-gluons with arbitrary polarisations.

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arXiv2020

Bosonic sectorized strings and the $(DF)^{2}$ theory

In this work, we investigate the bosonic chiral string in the sectorized interpretation, computing its spectrum, kinetic action and $3$-point amplitudes. As expected, the bosonic ambitwistor string is recovered in the tensionless limit. We also consider an extension of the bosonic model with current algebras. In that case, we compute the effective action and show that it is essentially the same as the action of the mass-deformed $(DF)^{2}$ theory found by Johansson and Nohle. Aspects which might seem somewhat contrived in the original construction --- such as the inclusion of a scalar transforming in some real representation of the gauge group --- are shown to follow very naturally from the worldsheet formulation of the theory.

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arXiv2019

Chiral strings, the sectorized description and their integrated vertex operators

A chiral string can be seen as an ordinary string in a singular gauge for the worldsheet metric and has the ambitwistor string as its tensionless limit. As proposed by Siegel, there is a one-parameter ($β$) gauge family interpolating between the chiral limit and the usual conformal gauge in string theory. This idea was used to compute scattering amplitudes of tensile chiral strings, which are given by standard string amplitudes with modified ($β$-dependent) antiholomorphic propagators. Due to the absence of a sensible definition of the integrated vertex operator, there is still no ordinary prescription for higher than $3$-point amplitude computations directly from the chiral model. The exception is the tensionless limit. In this work this gap will be filled. Starting with a chiral string action, the integrated vertex operator is defined, relying on the so-called sectorized interpretation. As it turns out, this construction effectively emulates a left/right factorization of the scattering amplitude and introduces a relative sign flip in the propagator for the sector-split target space coordinates. $N$-point tree-level amplitudes can be easily shown to coincide with the results of Siegel et al.

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arXiv2019

Towards the underlying gauge theory of the pure spinor superstring

Previous attempts to determine the worldsheet origin of the pure spinor formalism were not completely successful, but introduced important concepts that seem to be connected to its fundamental structure, e.g., emergent supersymmetry and the role of reparametrization symmetry. In this work, a new proposal towards the underlying gauge theory of the pure spinor superstring is presented, based on an extension of Berkovits' twistor-like constraint. The gauge algebra is analyzed in detail and worldsheet reparametrization is shown to be a redundant symmetry. The master action is built with a careful account of the intrinsic gauge symmetries associated with the pure spinor constraint and a consistent gauge fixing is performed. After a field redefinition, spacetime supersymmetry emerges and the resulting action describes the pure spinor superstring.

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arXiv2019

Quantization of the particle with a linear massless solution

In this work, a solution linear in the momentum for the massless constraint $P^{m}P_{m}=0$ is investigated. It is presented in terms of a $SO(2n,\mathbb{C})$ to $U(n)$ decomposition and interpreted in terms of projective pure spinors, which are known to parametrize the $\tfrac{SO(2n)}{U(n)}$ coset. The worldline action is quantized using the BRST formalism and, using the results of Berkovits and Cherkis, the ghost number zero wave function is shown to generate massless solutions for field equations of arbitrary spin. The model can be covariantly expressed by the action recently proposed in $D=10$ by Berkovits, in terms of a twistor-like constraint. However, a thorough account of its gauge symmetries does not lead to a spacetime supersymmetric theory. In order to derive from first principles the superparticle in the pure spinor formalism, a new model is proposed with partial worldline supersymmetry. The gauge algebra is then analyzed within the Batalin-Vilkovisky formalism and the gauge fixed action is finally shown to describe the pure spinor superparticle times a $U(1)$ decoupled sector.

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arXiv2017

Connecting the ambitwistor and the sectorized heterotic strings

The sectorized description of the (chiral) heterotic string using pure spinors has been misleadingly viewed as an infinite tension string. One evidence for this fact comes from the tree level 3-point graviton amplitude, which we show to contain the usual Einstein term plus a higher curvature contribution. After reintroducing a dimensionful parameter $\ell$ in the theory, we demonstrate that the heterotic model is in fact two-fold, depending on the choice of the supersymmetric sector, and that the spectrum also contains one massive (open string like) multiplet. By taking the $\ell\to\infty$ limit, we finally show that the ambitwistor string is recovered, reproducing the unexpected heterotic state in Mason and Skinner's RNS description.

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arXiv2016

Background constraints in the infinite tension limit of the heterotic string

In this work we investigate the classical constraints imposed on the supergravity and super Yang-Mills backgrounds in the $α'\to 0$ limit of the heterotic string using the pure spinor formalism. Guided by the recently observed sectorization of the model, we show that all the ten-dimensional constraints are elegantly obtained from the single condition of nilpotency of the BRST charge.

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arXiv2016

Notes on the ambitwistor pure spinor string

In this work, some aspects of the ambitwistor pure spinor string are investigated. The $b$ ghost is presented and its main properties are derived in a simple way, very similar to the usual pure spinor $b$ ghost construction. The heterotic case is also addressed with a new proposal for the BRST charge. The BRST cohomology is shown to correctly describe the heterotic supergravity spectrum and a semi-composite $b$ ghost is constructed.

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arXiv2015

Spectrum generating algebra for the pure spinor superstring

In this work, a DDF-like construction within the pure spinor formalism is presented. Starting with the light-cone massless vertices, the creation/annihilation algebra is derived in a simple manner, enabling a systematic construction of the physical vertex operators at any mass level in terms of $SO\left(8\right)$ superfields, in both integrated and unintegrated forms.

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arXiv2015

On the field-antifield (a)symmetry of the pure spinor superstring

In this work, the DDF-like approach to the pure spinor cohomology is extended to the next ghost number level, the so called antifields. In a direct (supersymmetric) parallel to the bosonic string, some properties of the ghost number two cohomology are derived with the enlargement of the DDF algebra. Also, the DDF conjugates of the b ghost zero mode emerge naturally from the extended algebra and the physical state condition is discussed. Unlike the bosonic string case, the cohomology analysis of the pure spinor b ghost is restricted to BRST-closed states.

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arXiv2014

Light-Cone Analysis of the Pure Spinor Formalism for the Superstring

Physical states of the superstring can be described in light-cone gauge by acting with transverse bosonic $α_{-n}^{j}$ and fermionic $\bar{q}_{-n}^{\dot{a}}$ operators on an $SO\left(8\right)$-covariant superfield where $j,\dot{a}=1$ to $8$. In the pure spinor formalism, these states are described in an $SO\left(9,1\right)$-covariant manner by the cohomology of the BRST charge $Q=\frac{1}{2πi}\ointλ^αd_α$. In this paper, a similarity transformation is found which simplifies the form of $Q$ and maps the light-cone description of the superstring vertices into DDF-like operators in the cohomology of $Q$.

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arXiv2013

Notes on the pure spinor b ghost

In this work, a particular BRST-exact class of deformations of the b ghost in the non-minimal pure spinor formalism is investigated and the impact of this construction in the $\mathcal{N}=2$ $\hat{c}=3$ topological string algebra is analysed. As an example, a subclass of deformations is explicitly shown, where the U(1) current appears in a conventional form, involving only the ghost number currents. Furthermore, a c ghost like composite field is introduced, but with an unusual construction.

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arXiv2013

Nilpotency of the b ghost in the non-minimal pure spinor formalism

The b ghost in the non minimal pure spinor formalism is not a fundamental field. It is based on a complicated chain of operators and proving its nilpotency is nontrivial. Chandia proved this property in arXiv:1008.1778, but with an assumption on the non-minimal variables that is not valid in general. In this work, the b ghost is demonstrated to be nilpotent without this assumption.

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