Soft sub-leading divergences in Yang-Mills amplitudes

In this short note I show that the soft limit for colour-ordered tree-level Yang-Mills amplitudes contains a sub-leading divergent term analogous to terms found recently by Cachazo and Strominger for tree-level gravity amplitudes

Complexity computation for compact 3-manifolds via crystallizations and Heegaard diagrams

The idea of computing Matveev complexity by using Heegaard decompositions has been recently developed by two different approaches: the first one for closed 3-manifolds via crystallization theory, yielding the notion of Gem-Matveev complexity; the other one for compact orientable 3-manifolds via generalized Heegaard diagrams, yielding the notion of modified Heegaard complexity. In this paper we extend to the non-orientable case the definition of modified Heegaard complexity and prove that for closed 3-manifolds Gem-Matveev complexity and modified Heegaard complexity coincide. Hence, they turn out to be useful different tools to compute the same upper bound for Matveev complexity.Comment: 12 pages; accepted for publication in Topology and Its Applications, volume containing Proceedings of Prague Toposym 201

Infrared behaviour of the one-loop scattering equations and supergravity integrands

The recently introduced ambitwistor string led to a striking proposal for one-loop maximal supergravity amplitudes, localised on the solutions of the ambitwistor one-loop scattering equations. However, these amplitudes have not yet been explicitly analysed due to the apparent complexity of the equations that determine the localisation. In this paper we propose an analytic solution to the four-point one-loop scattering equations in the infrared (IR) regime of the amplitude. Using this solution, we compute the ambitwistor integrand and demonstrate that it correctly reproduces the four-graviton integrand, in the IR regime. This solution qualitatively extends to n points. To conclude, we explain that the ambitwistor one-loop scattering equations actually correspond to the standard Gross & Mende saddle point.Comment: 23 pages, 5 figure

Windings of twisted strings

Twistor string models have been known for more than a decade now but have come back under the spotlight recently with the advent of the scattering equation formalism which has greatly generalized the scope of these models. A striking ubiquitous feature of these models has always been that, contrary to usual string theory, they do not admit vibrational modes and thus describe only conventional field theory. In this paper we report on the surprising discovery of a whole new sector of one of these theories which we call "twisted strings," when spacetime has compact directions. We find that the spectrum is enhanced from a finite number of states to an infinite number of interacting higher spin massive states. We describe both bosonic and world sheet supersymmetric models, their spectra and scattering amplitudes. These models have distinctive features of both string and field theory, for example they are invariant under stringy T-duality but have the high energy behavior typical of field theory. Therefore they describe a new kind of field theories in target space, sitting on their own halfway between string and field theory.Comment: 6 pages. v2 : a few clarifications and references added. v3 : published PRD versio

On the null origin of the ambitwistor string

In this paper we present the null string origin of the ambitwistor string. Classically, the null string is the tensionless limit of string theory, and so too is the Ambitwistor string. Both have as constraint algebra the Galilean Conformal Algebra in two dimensions. But something interesting happens in the quantum theory since there is an ambiguity in quantizing the null string. We show that, given a particular choice of quantization scheme and a particular gauge, the null string coincides with the ambitwistor string both classically and quantum mechanically. We also show that the same holds for the spinning versions of the null string and Ambitwistor string. With these results we clarify the relationship between the Ambitwistor string, the null string, the usual string and the Hohm-Siegel-Zwiebach theory.Comment: 22 pages, 1 figur

Analysis of the structural correlates for antibody polyreactivity by multiple reassortments of chimeric human immunoglobulin heavy and light chain V segments.

Polyreactive antibodies (Abs) constitute a major proportion of the early Ab repertoire and are an important component of the natural defense mechanisms against infections. They are primarily immunoglobulin M (IgM) and bind a variety of structurally dissimilar self and exogenous antigens (Ags) with moderate affinity. We analyzed the contribution of Ig polyvalency and of heavy (H) and light (L) chain variable (V) regions to polyreactivity in recombinatorial experiments involving the VH-diversity(D)-JH and V kappa-J kappa gene segments of a human polyreactive IgM, monoclonal antibody 55 (mAb55), and those of a human monoreactive anti-insulin IgG, mAb13, in an in vitro C gamma l and C kappa human expression system. These mAbs are virtually identical in their VH and V kappa gene segment sequences. First, we expressed the VH-D-JH and V kappa-J kappa genes of the IgM mAb55 as V segments of an IgG molecule. The bivalent recombinant IgG Ab bound multiple Ags with an efficiency only slightly lower than that of the original decavalent IgM mAb55, suggesting that class switch to IgG does not affect the Ig polyreactivity. Second, we coexpressed the mAb55-derived H or kappa chain with the mAb13-derived kappa or H chain, respectively. The hybrid IgG Ab bearing the mAb55-derived H chain V segment paired with the mAb13-derived kappa V segment, but not that bearing the mAb13-derived H chain V segment paired with the mAb55-derived kappa V segment, bound multiple Ags, suggesting that the Ig H chain plays a major role in the Ig polyreactivity. Third, we shuffled the framework 1 (FR1)-FR3 and complementarity determining region 3 (CDR3) regions of the H and kappa chain V segments of the mAB55-derived IgG molecule with the corresponding regions of the monoreactive IgG mAb13. The mAb55-derived IgG molecule lost polyreactivity when the H chain CDR3, but not the FR1-FR3 region, was replaced by the corresponding region of mAb13, suggesting that within the H chain, the CDR3 provides the major structural correlate for multiple Ag-binding. This was formally proved by the multiple Ag-binding of the originally monoreactive mAb13-derived IgG molecule grafted with the mAb55-derived H chain CDR3. The polyreactivity of this chimeric IgG was maximized by grafting of the mAb55-derived kappa chain FR1-FR3, but not that of the kappa chain CDR3.(ABSTRACT TRUNCATED AT 400 WORDS

Cataloguing PL 4-manifolds by gem-complexity

We describe an algorithm to subdivide automatically a given set of PL n-manifolds (via coloured triangulations or, equivalently, via crystallizations) into classes whose elements are PL-homeomorphic. The algorithm, implemented in the case n=4, succeeds to solve completely the PL-homeomorphism problem among the catalogue of all closed connected PL 4-manifolds up to gem-complexity 8 (i.e., which admit a coloured triangulation with at most 18 4-simplices). Possible interactions with the (not completely known) relationship among different classification in TOP and DIFF=PL categories are also investigated. As a first consequence of the above PL classification, the non-existence of exotic PL 4-manifolds up to gem-complexity 8 is proved. Further applications of the tool are described, related to possible PL-recognition of different triangulations of the K3-surface.Comment: 25 pages, 5 figures. Improvements suggested by the refere

Computing Matveev's complexity via crystallization theory: the boundary case

The notion of Gem-Matveev complexity has been introduced within crystallization theory, as a combinatorial method to estimate Matveev's complexity of closed 3-manifolds; it yielded upper bounds for interesting classes of such manifolds. In this paper we extend the definition to the case of non-empty boundary and prove that for each compact irreducible and boundary-irreducible 3-manifold it coincides with the modified Heegaard complexity introduced by Cattabriga, Mulazzani and Vesnin. Moreover, via Gem-Matveev complexity, we obtain an estimation of Matveev's complexity for all Seifert 3-manifolds with base $\mathbb D^2$ and two exceptional fibers and, therefore, for all torus knot complements.Comment: 27 pages, 14 figure

Lower bounds for regular genus and gem-complexity of PL 4-manifolds

Within crystallization theory, two interesting PL invariants for $d$-manifolds have been introduced and studied, namely {\it gem-complexity} and {\it regular genus}. In the present paper we prove that, for any closed connected PL $4$-manifold $M$, its gem-complexity $\mathit{k}(M)$ and its regular genus $\mathcal G(M)$ satisfy: $$\mathit{k}(M) \ \geq \ 3 \chi (M) + 10m -6 \ \ \ \text{and} \ \ \ \mathcal G(M) \ \geq \ 2 \chi (M) + 5m -4,$$ where $rk(\pi_1(M))=m.$ These lower bounds enable to strictly improve previously known estimations for regular genus and gem-complexity of product 4-manifolds. Moreover, the class of {\it semi-simple crystallizations} is introduced, so that the represented PL 4-manifolds attain the above lower bounds. The additivity of both gem-complexity and regular genus with respect to connected sum is also proved for such a class of PL 4-manifolds, which comprehends all ones of "standard type", involved in existing crystallization catalogues, and their connected sums.Comment: 17 pages, 3 figures. To appear in Forum Mathematicu