Disk Amplitudes Research Articles

Towards massive field-theory amplitudes from the cohomology of pure spinor superspace

By analogy with the formula for the massless string disk amplitudes, we define massive field-theory tree amplitudes and conjecture that the BRST cohomology structure of pure spinor superspace fixes their form. We give evidence by deriving the pure spinor superspace expression of the massive field-theory n-point tree amplitude with one first-level massive and n − 1 massless states in two ways: 1) from BRST cohomology arguments in pure spinor superspace and 2) from the α′2 correction to the massless string amplitudes by inverting the unitarity constraint in superspace.

The cylinder amplitude in the hard dimer model on 2D causal dynamical triangulations

We consider the model of hard dimers coupled to two-dimensional causal dynamical triangulations (CDT) with all dimer types present and solve it exactly subject to a single restriction. Depending on the dimer weights there are, in addition to the usual gravity phase of CDT, two tri-critical and two dense dimer phases. We establish the properties of these phases, computing their cylinder and disk amplitudes, and their scaling limits.

KK-like relations of α′ corrections to disk amplitudes

Inspired by the definition of color-dressed amplitudes in string theory, we define analogous color-dressed permutations replacing the color-ordered string amplitudes by their corresponding permutations. Decomposing the color traces into symmetrized traces and structure constants, the color-dressed permutations define BRST-invariant permutations, which we show are elements of the inverse Solomon descent algebra and we find a closed formula for them. We then present evidence that these permutations encode KK-like relations among the different α′ corrections to the disk amplitudes refined by their MZV content. In particular, the number of linearly independent amplitudes at a given α′ order and MZV content is given by (sums of) Stirling cycle numbers. In addition, we show how the superfield expansion of BRST invariants of the pure spinor formalism corresponding to α′2ζ2 corrections is encoded in the descent algebra.

D-branes in AdS3 \xd7 S3 \xd7 \U0001d54b4 at k = 1 and their holographic duals

String theory on AdS3× S3× \U0001d54b4 with minimal k = 1 NS-NS flux can be described in terms of a free field worldsheet theory in the hybrid formalism. We construct various D-branes of this string theory and calculate their associated cylinder amplitudes. We find that these amplitudes match with the cylinder correlators of certain boundary states of the dual symmetric orbifold CFT Sym(\U0001d54b4), thus suggesting a direct correspondence between these boundary conditions. We also show that the disk amplitudes of these D-branes localise to those points in the worldsheet moduli space where the worldsheet disk holomorphically covers the spacetime disk.

Proof of new S-matrix formula from classical solutions in open string field theory: Or, deriving on-shell open string field amplitudes without using Feynman rules, Part II

Abstract We study the relation between the gauge-invariant quantity obtained by T. Masuda and H. Matsunaga (arXiv:1908.09784) and the Feynman diagrams in the dressed $\mathcal {B}_0$ gauge in the open cubic string field theory. We derive a set of recurrence relations that hold among the terms of this gauge-invariant quantity. By using these relations, we prove that this gauge-invariant quantity equals the S-matrix at the tree level. We also present a proof that a set of new Feynman rules proposed by T. Masuda and H. Matsunaga (arXiv:2003.05021) reproduces the on-shell disk amplitudes correctly by using the same combinatorial identities.

Closed string disk amplitudes in the pure spinor formalism

We evaluate closed string disk amplitudes in the pure spinor formalism. We focus on low point functions (two- and one-point functions) but our analysis is also relevant for higher n-point functions. Amongst others we discuss issues arising due to the gauge fixing of the conformal Killing group of the disk and due to the zero mode prescription in the pure spinor formalism. As expected, in the end we find agreement with the known results from the RNS formalism.

On brane curvature couplings from disk amplitude

The Chern–Simons coupling on D-branes in string theory is known to receive higher derivative corrections which include the curvature tensor and the Neveu–Schwarz B-field. We find some curvature couplings of D-branes to closed string fields by evaluating string theory disc amplitudes of one Ramond–Ramond field C(p+1) and two gravitons in the presence of a single Dp-brane in type II string theory.

New relations for Einstein–Yang–Mills amplitudes

We obtain new relations between Einstein–Yang–Mills (EYM) amplitudes involving N gauge bosons plus a single graviton and pure Yang–Mills amplitudes involving N gauge bosons plus one additional vector boson inserted in a way typical for a gauge boson of a “spectator” group commuting with the group associated to original N gauge bosons. We show that such EYM amplitudes satisfy U(1) decoupling relations similar to Kleiss–Kuijf relations for Yang–Mills amplitudes. We consider a D-brane embedding of EYM amplitudes in the framework of disk amplitudes involving open and closed strings. A new set of monodromy relations is derived for mixed open–closed amplitudes with one closed string inserted on the disk world-sheet and a number of open strings at the boundary. These relations allow expressing the latter in terms of pure open string amplitudes and, in the field-theory limit, they yield the U(1) decoupling relations for EYM amplitudes.

Direct generation of a Majorana mass for the neutron from exotic instantons

We discuss a new mechanism in which non-perturbative quantum gravity effects directly generate a Majorana mass for the neutron. In particular, in string theory, exotic instantons can generate an effective six quark operator by calculable mixed disk amplitudes. In a low string scale scenario, with $M_{S}\simeq 10\div 10^{5}\, \rm TeV$, a neutron-antineutron oscillation can be reached in the next generation of experiments. we argue that protons and neutralinos are not destabilized and that dangerous FCNCs are not generated. We show an example of quiver theories, locally free by tadpoles and anomalies, reproducing MSSM plus a Majorana neutron and a Majorana neutrino. These models naturally provide a viable baryogenesis mechanism by resonant RH neutrino decays, as well as a stable WIMP-like dark matter. We also discuss how LHC data will provide useful inputs for our model, in the immediate future, testing several different regions of the parameter space. Such a mechanism represents a simple and calculable counter-example to the Wilsonian UV completion of effective non-renormalizable operators.

Three-point disc amplitudes in the RNS formalism

We calculate all tree level string theory vacuum to Dp-brane disc amplitudes involving an arbitrary RR-state and two NS–NS vertex operators. This computation was earlier performed by K. Becker, Guo, and Robbins for the simplest case of a RR-state of type C(p−3). Here we use the aid of a computer to calculate all possible three-point amplitudes involving a RR-vertex operator of type C(p+1+2k).

Disk scattering of open and closed strings (I)

At the tree level, the scattering processes involving open and closed strings are described by a disk world-sheet with vertex operator insertions at the boundary and in the bulk. Such amplitudes can be decomposed as certain linear combinations of pure open string amplitudes. While previous relations have been established on the double cover (complex sphere) in this letter we derive them on the disk (upper complex half plane) allowing for different momenta of the left- and right-movers of the closed string. Formally, the computation of disk amplitudes involving both open and closed strings is reduced to considering the monodromies on the underlying string world-sheet.

On the soft limit of open string disk amplitudes with massive states

We discuss the soft behaviour of open string amplitudes with gluons and massive states in any dimension. Notwithstanding non-minimal couplings of massive higher spin states to gluons, relying on OPE and factorization, we argue that the leading and subleading terms are universal and identical to the ones in Yang-Mills theories. In order to illustrate this, we compute some 4-point amplitudes on the disk involving gluons, massive states and, for the bosonic string, tachyons. For the superstring, we revisit the structure of the massive super-multiplets at the first massive level and rewrite the amplitudes in D = 4 in the spinor helicity formalism, that we adapt to accommodate massive higher spin states. We also check the validity of a recently obtained formula relating open superstring amplitudes for mass-less states at tree-level to SYM amplitudes, by factorisation on two-particle massive poles. Finally we analyse the holomorphic soft limit of superstring amplitudes with one massive insertion.

RNS derivation of N-point disk amplitudes from the revisited S-matrix approach

Recently, in [7] we proposed a revisited S-matrix approach to efficiently find the bosonic terms of the open superstring low energy effective lagrangian (OSLEEL). This approach allows to compute the α′N terms of the OSLEEL using open superstring n-point amplitudes in which n is considerably lower than (N+2) (which is the order of the required amplitude to obtain those α′N terms by means of the conventional S-matrix approach). In this work we use our revisited S-matrix approach to examine the structure of the scattering amplitudes, arriving at a closed form for them. This is a RNS derivation of the formula first found by Mafra, Schlotterer and Stieberger [21], using the pure spinor formalism. We have succeeded doing this for the 5, 6 and 7-point amplitudes. In order to achieve these results we have done a careful analysis of the kinematical structure of the amplitudes, finding as a by-product a purely kinematical derivation of the BCJ relations (for N=4,5,6 and 7). Also, following the spirit of the revisited S-matrix approach, we have found the α′ expansions for these amplitudes up to α′6 order in some cases, by only using the well known open superstring 4-point amplitude, cyclic symmetry and tree level unitarity: we have not needed to compute any numerical series or any integral involving polylogarithms, at any moment.

The structure of the term in type IIB string theory

Based on the structure of the on-shell linearized superspace of type IIB supergravity, we argue that there is a non-BPS 16 derivative interaction in the effective action of type IIB string theory of the form (t8t8R4)2, which we call the interaction. It lies in the same supermultiplet as the interaction. Using the Kawai–Lewellen–Tye relation, we analyze the structure of the tree level eight-graviton scattering amplitude in the type IIB theory, which leads to the interaction at the linearized level. This involves an analysis of color-ordered multi-gluon disc amplitudes in the type I theory, which shows an intricate pole structure and transcendentality consistent with various other interactions. Considerations of S-duality show that the interaction receives non-analytic contributions in the string coupling at one and two loops. Apart from receiving perturbative contributions, we show that the interaction receives a non-vanishing contribution in the one D-instanton-anti-instanton background at leading order in the weak coupling expansion.

Topological strings, D-model, and knot contact homology

We study the connection between topological strings and contact homology recently proposed in the context of knot invariants. In particular, we establish the proposed relation between the Gromov-Witten disk amplitudes of a Lagrangian associated to a knot and augmentations of its contact homology algebra. This also implies the equality between the Q-deformed A-polynomial and the augmentation polynomial of knot contact homology (in the irreducible case). We also generalize this relation to the case of links and to higher rank representations for knots. The generalization involves a study of the quantum moduli space of special Lagrangian branes with higher Betti numbers probing the Calabi-Yau. This leads to an extension of SYZ, and a new notion of mirror symmetry, involving higher dimensional mirrors. The mirror theory is a topological string, related to D-modules, which we call the "D-model." In the present setting, the mirror manifold is the augmentation variety of the link. Connecting further to contact geometry, we study intersection properties of branches of the augmentation variety guided by the relation to D-modules. This study leads us to propose concrete geometric constructions of Lagrangian fillings for links. We also relate the augmentation variety with the large N limit of the colored HOMFLY, which we conjecture to be related to a Q-deformation of the extension of A-polynomials associated with the link complement.

Non-perturbative gauge/gravity correspondence in $ \mathcal{N} $ = 2 theories

We derive the exact supergravity profile for the twisted scalar field emitted by a system of fractional D3 branes at a $ {\mathbb{Z}_2} $ orbifold singularity supporting $ \mathcal{N} $ = 2 quiver gauge theories with unitary groups and bifundamental matter. At the perturbative level this twisted field is “dual” to the gauge coupling but it is corrected non-perturbatively by an infinite tower of fractional D-instantons. The explicit microscopic description allows to derive the gravity profile from disk amplitudes computing the emission rate of the twisted scalar field in terms of chiral correlators in the dual gauge theory. We compute these quantum correlators using multi-instanton localization techniques and/or Seiberg-Witten analysis. Finally, we discuss a non-perturbative relation between the twisted scalar and the effective coupling of the gauge theory for some simple choices of the brane set ups.

Deformed planar topological open string amplitudes on Seiberg-Witten curve

We study refined B-model via the beta ensemble of matrix models. Especially, for four dimensional N=2 SU(2) supersymmetric gauge theories with N_f=0,1 and 2 fundamental flavors, we discuss the correspondence between deformed disk amplitudes on each Seiberg-Witten curve and the Nekrasov-Shatashvili limit of the corresponding irregular one point block of a degenerate operator via the AGT correspondence. We also discuss the relation between deformed annulus amplitudes and the irregular two point block of the degenerate operator, and check a desired agreement for N_f=0 and 1 cases.

Disc amplitudes, picture changing and space-time actions

We study in detail the procedure for obtaining couplings of D-branes to closed string fields by evaluating string theory disc amplitudes. We perform a careful construction of the relevant vertex operators and discuss the effects of inserting the boundary state which encodes the presence of the D-brane. We confront the issue of non-decoupling of BRST-exact states and prove that the problem is evaded for the computations we need, thus demonstrating that our amplitudes are automatically gauge-invariant and independent of the distribution of picture charge. Finally, we compute explicitly the two-point amplitudes of two NS-NS fields or one NS-NS and one R-R field on the disc, and we carefully compare all the lowest order terms with predictions from supergravity.

New D1-D5-P geometries from string amplitudes

We derive the long range supergravity fields sourced by a D1-D5-P bound state from disk amplitudes for massless closed string emission. We suggest that since the parameter controlling the string perturbation expansion for this calculation decreases with distance from the bound state, the resulting asymptotic fields are valid even in the regime of parameters in which there is a classical black hole solution with the same charges. The supergravity fields differ from the black hole solution by multipole moments and are more general than those contained within known classes of solutions in the literature, whilst still preserving four supersymmetries. Our results support the conjecture that the black hole solution should be interpreted as a coarse-grained description rather than an exact description of the gravitational field sourced by D1-D5-P bound states in this regime of parameters.

= 2 Instanton Effective action in Ω-background and D3/D(−1)-brane System in R-R background

We study the relation between the ADHM construction of instantons in the Ω-background and the fractional D3/D(−1)-branes at the orbifold singularity of ℂ × ℂ2/ℤ2 in Ramond-Ramond (R-R) 3-form field strength background. We calculate disk amplitudes of open strings connecting the D3/D(−1)-branes in certain R-R background to obtain the D(−1)-brane effective action deformed by the R-R background. We show that the deformed D(−1)-brane effective action agrees with the instanton effective action in the Ω-background.