One-loop masses of Neumann-Dirichlet open strings and boundary-changing vertex operators

We derive the masses acquired at one loop by massless scalars in the Neumann-Dirichlet sector of open strings, when supersymmetry is spontaneously broken. It is done by computing two-point functions of “boundary-changing vertex operators” inserted on the boundaries of the annulus and Möbius strip. This requires the evaluation of correlators of “excited boundary-changing fields,” which are analogous to excited twist fields for closed strings. We work in the type IIB orientifold theory compactified on T2× T4/ℤ2, where $$ \mathcal{N} $$ N = 2 supersymmetry is broken to $$ \mathcal{N} $$ N = 0 by the Scherk-Schwarz mechanism implemented along T2. Even though the full expression of the squared masses is complicated, it reduces to a very simple form when the lowest scale of the background is the supersymmetry breaking scale M3/2. We use our results to analyze in this regime the stability at the quantum level of the moduli fields arising in the Neumann-Dirichlet sector. This completes the study of ref. [32], where the quantum masses of all other types of moduli arising in the open- or closed-string sectors are derived. Ultimately, we identify all brane configurations that produce backgrounds without tachyons at one loop and yield an effective potential exponentially suppressed, or strictly positive with runaway behavior of M3/2.

Worldline description of a bi-adjoint scalar and the zeroth copy

Bi-adjoint scalars are helpful in studying properties of color/kinematics duality and the double copy, which relates scattering amplitudes of gauge and gravity theories. Here we study bi-adjoint scalars from a worldline perspective. We show how a global G × $$ \overset{\sim }{G} $$ G ~ symmetry group may be realized by worldline degrees of freedom. The worldline action gives rise to vertex operators, which are compared to similar ones describing the coupling to gauge fields and gravity, thus exposing the color/kinematics interplay in this framework. The action is quantized by path integrals to find a worldline representation of the one-loop QFT effective action of the bi-adjoint scalar cubic theory. As simple applications, we recover the one-loop beta function of the theory in six dimensions, verifying its vanishing, and compute the self-energy correction to the propagator. The model is easily extendable to that of a particle carrying an arbitrary representation of direct products of global symmetry groups, including the multi-adjoint particle, whose one-loop beta function we reproduce as well.

Green-Schwarz and pure spinor formulations of chiral strings

Bosonic and RNS chiral strings have been defined from a singular gauge fixing of the respective Polyakov and spinning string actions, enforcing, among other things, the finite nature of their physical spectra. Except for the heterotic case, the tensionless limits of such chiral models have been shown to describe the same field theories predicted by their ambitwistor analogues. In this paper, we study the Green-Schwarz formulation for Type II and heterotic superstrings in a singular gauge. After performing a light-cone gauge analysis, their physical spectra are shown to match those of RNS chiral strings, and their respective tensionless limits are found to describe the same field theories predicted by RNS ambitwistor strings. Their pure spinor counterparts are then introduced by making use of the Oda-Tonin method. In doing so, symmetries hidden in the pure spinor ambitwistor string action become manifest, proposals motivating the sectorized pure spinor BRST charges find simple grounds, and integrated vertex operators emerge naturally.

Two-point functions of Neumann–Dirichlet open-string sector moduli

In this paper, we compute at one loop the two-point functions of massless scalars in the Neumann–Dirichlet open-string sector of the type IIB orientifold compactified on [Formula: see text], when [Formula: see text] supersymmetry is spontaneously broken. This is done by evaluating correlation functions of “boundary-changing vertex operators” which are analogous to correlators of twist fields for closed strings. We use our results to compute the mass developed at one loop by the moduli fields arising in the Neumann–Dirichlet sector.

The AdS3 × S1 chiral ring

We study AdS3× S1× Y supersymmetric string theory backgrounds with Neveu-Schwarz-Neveu-Schwarz flux that are dual to $$ \mathcal{N} $$ N = 2 superconformal theories on the boundary. We classify all worldsheet vertex operators that correspond to space-time chiral primaries. We compute space-time chiral ring structure constants for operators in the zero spectral flow sector using the operator product expansion in the worldsheet theory. We find that the structure constants take a universal form that depends only on the topological data of the $$ \mathcal{N} $$ N = 2 superconformal theory on Y.

The physical states of the Hybrid Formalism

String theory on AdS3 × S3 × $$ \mathbbm{T} $$ T 4 with one unit (k = 1) of NS-NS flux is considered in the hybrid formalism of Berkovits, Vafa & Witten (BVW). Using the free field realisation of the world-sheet theory at k = 1, we identify explicitly the BRST cohomology classes corresponding to some of the low-lying states of the dual CFT. In particular, we do this for the $$ \mathcal{N} $$ N = 4 superconformal generators of the symmetric orbifold theory, and we confirm these identifications by showing that the worldsheet correlators reproduce the expected dual CFT answer. Along the way we note that the physical vertex operators on the worldsheet have a simpler form if one works with a different, but equivalent, choice for the BRST operators relative to BVW.

Intersecting defects in gauge theory, quantum spin chains, and Knizhnik-Zamolodchikov equations

We propose an interesting BPS/CFT correspondence playground: the correlation function of two intersecting half-BPS surface defects in four-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric SU(N) gauge theory with 2N fundamental hypermultiplets. We show it satisfies a difference equation, the fractional quantum T-Q relation. Its Fourier transform is the 5-point conformal block of the $$ {\hat{\mathfrak{sl}}}_N $$ sl ̂ N current algebra with one of the vertex operators corresponding to the N-dimensional $$ {\mathfrak{sl}}_N $$ sl N representation, which we demonstrate with the help of the Knizhnik-Zamolodchikov equation. We also identify the correlator with a state of the $$ {XXX}_{{\mathfrak{sl}}_2} $$ XXX sl 2 spin chain of N Heisenberg-Weyl modules over Y ($$ {\mathfrak{sl}}_2 $$ sl 2 ). We discuss the associated quantum Lax operators, and connections to isomonodromic deformations.

AdS 5 × S5 supergravity vertex operators

In any type II superstring background, the supergravity vertex operators in the pure spinor formalism are described by a gauge superfield. In this paper, we obtain for the first time an explicit expression for this superfield in an AdS5 × S5 background. Previously, the vertex operators were only known close to the boundary of AdS5 or in the minus eight picture. Our strategy for the computation was to apply eight picture raising operators in the minus eight picture vertices. In the process, a huge number of terms are generated and we have developed numerical techniques to perform intermediary simplifications. Alternatively, the same numerical techniques can be used to compute the vertices directly in the zero picture by constructing a basis of invariants and fitting for the coefficients. One motivation for constructing the vertex operators is the computation of AdS5 × S5 string amplitudes.

The structure of IR divergences in celestial gluon amplitudes

The all-loop resummation of SU(N) gauge theory amplitudes is known to factorize into an IR-divergent (soft and collinear) factor and a finite (hard) piece. The divergent factor is universal, whereas the hard function is a process-dependent quantity.We prove that this factorization persists for the corresponding celestial amplitudes. Moreover, the soft/collinear factor becomes a scalar correlator of the product of renormalized Wilson lines defined in terms of celestial data. Their effect on the hard amplitude is a shift in the scaling dimensions by an infinite amount, proportional to the cusp anomalous dimension. This leads us to conclude that the celestial-IR-safe gluon amplitude corresponds to a expectation value of operators dressed with Wilson line primaries. These results hold for finite N.In the large N limit, we show that the soft/collinear correlator can be described in terms of vertex operators in a Coulomb gas of colored scalar primaries with nearest neighbor interactions. In the particular cases of four and five gluons in planar $$ \mathcal{N} $$ N = 4 SYM theory, where the hard factor is known to exponentiate, we establish that the Mellin transform converges in the UV thanks to the fact that the cusp anomalous dimension is a positive quantity. In other words, the very existence of the full celestial amplitude is owed to the positivity of the cusp anomalous dimension.

The large-c Virasoro identity block is a semi-classical Liouville correlator

It will be shown analytically that the light sector of the identity block of a mixed heavy-light correlator in the large central charge limit is given by a correlation function of light operators on an effective background geometry. This geometry is generated by the presence of the heavy operators. It is shown that this background geometry is a solution to the Liouville equation of motion sourced by corresponding heavy vertex operators and subsequently that the light sector of the identity block matches the Liouville correlation function in the semi-classical limit. This method effectively captures the spirit of Einstein gravity as a theory of dynamical geometry in AdS/CFT. The reason being that Liouville theory is closely related to semi-classical asymptotically AdS3 gravity.