We compute a class of gauge invariant observables for marginal solutions and the tachyon vacuum. In each case we find that the observables are related in a simple way to the closed-string tadpole on a disk with appropriate boundary conditions. We give a sketch of an argument that this result should hold in general using the BRST invariance of the closed string two-point function. Finally, we discuss the analogous set of invariants in the Berkovits superstring field theory.
While R-R tadpoles should be canceled for consistency, string models with broken supersymmetry generally have uncanceled NS-NS tadpoles. Their presence signals that the background does not solve the field equations, so that these models are in "wrong" vacua. In this letter we investigate, with reference to some prototype examples, whether the true values of physical quantities can be recovered resumming the NS-NS tadpoles, hence by an approach that is related to the analysis based on String Field Theory by open-closed duality. We show that, indeed, the positive classical vacuum energy of a Dp-…
We investigate the quantum structure of Witten's cubic open bosonic string field theory by computing the one-loop contribution to the open string tadpole using both oscillator and conformal field theory methods. We find divergences and a breakdown of BRST invariance in the tadpole diagram arising from tachyonic and massless closed string states, and we discuss ways of treating these problems. For a Dp-brane with sufficiently many transverse dimensions, the tadpole can be rendered finite by analytically continuing the closed string tachyon by hand; this diagram then naturally incorporates the (…
The tachyon-free nonsupersymmetric string theories in ten dimensions have dilaton tadpoles which forbid a Minkowski vacuum. We determine the maximally symmetric backgrounds for the $USp(32)$ Type I string and the $SO(16)\times SO(16)$ heterotic string. The static solutions exhibit nine dimensional Poincaré symmetry and have finite 9D Planck and Yang-Mills constants. The low energy geometry is given by a ten dimensional manifold with two boundaries separated by a finite distance which suggests a spontaneous compactification of the ten dimensional string theory.
We consider string theory vacua with tadpoles for dynamical fields and uncover universal features of the resulting spacetime-dependent solutions. We argue that the solutions can extend only a finite distance $Δ$ away in the spacetime dimensions over which the fields vary, scaling as $Δ^n\sim {\cal T}$ with the strength of the tadpole ${\cal T}$. We show that naive singularities arising at this distance scale are physically replaced by ends of spacetime, related to the cobordism defects of the swampland cobordism conjecture and involving stringy ingredients like orientifold planes and branes, o…
We study the topological string on compact Calabi-Yau threefolds in the presence of orientifolds and D-branes. In examples, we find that the total topological string amplitude admits a BPS expansion only if the topological charge of the D-brane is equal to that of the orientifold plane. We interpret this as a manifestation of a general tadpole cancellation condition in the topological string that is necessary for decoupling of A- and B-model in loop amplitudes. Our calculations in the A-model involve an adapted version of existing localization techniques, and give predictions for the real enum…
In this paper we analyze the problem of tadpole cancellation in open topological strings. We prove that the inclusion of unorientable worldsheet diagrams guarantees a consistent decoupling of A and B model for open superstring amplitudes at all genera. This is proven by direct microscopic computation in Super Conformal Field Theory. For the B-model we explicitly calculate one loop amplitudes in terms of analytic Ray-Singer torsions of appropriate vector bundles and obtain that the decoupling corresponds to the cancellation of D-brane and orientifold charges. Local tadpole cancellation on the w…
Closed string theories on orbifolds contain both untwisted and twisted states. The latter are normally assumed to live exactly at the orbifold fixed points. We perform a calculation of a gauge field tadpole amplitude and show that off-shell both the twisted and untwisted states give rise to non-trivial momentum profiles over the orbifold C^3/Z_3. These profiles take the form of Gaussian distributions integrated over the fundamental domain of the modular parameter of the torus. The propagators of the internal coordinate fields on the torus world sheet determine the width of the Gaussian profile…
We compute the off-shell 1-loop tadpole amplitude in heterotic string field theory. With a special choice of cubic vertex, we show that this amplitude can be computed exactly. We obtain explicit and elementary expressions for the Feynman graph decomposition of the moduli space, the local coordinate map at the puncture as a function of the modulus, and the $b$-ghost insertions needed for the integration measure. Recently developed homotopy algebra methods provide a consistent configuration of picture changing operators. We discuss the consequences of spurious poles for the choice of picture cha…
This Thesis discusses a number of issues related to the problem of tadpoles and vacuum redefinitions that the breaking of supersymmetry brings about in String Theory. The idea pursued here is to try to formulate the theory in a ``wrong'' vacuum (the vacuum that one naively identifies prior to the redefinitions) and, gaining some intuition from some simpler field theory settings, try to set up a calculational scheme for vacuum redefinitions in String Theory. This requires in general complicated resummations, but some simpler cases can be identified. This is true, in principle, for models with f…
Orbifolds in field theory are potentially singular objects for at their fixed points the curvature becomes infinite, therefore one may wonder whether field theory calculations near orbifold singularities can be trusted. String theory is perfectly well defined on orbifolds and can therefore be taken as a UV completion of field theory on orbifolds. We investigate the properties of field and string theory near orbifold singularities by reviewing the computation of a one loop gauge field tadpole. We find that in string theory the twisted states give contributions that have a spread of a couple of …
We study non perturbative superpotentials for N=1 super Yang Mills from the point of view of large $N$ dualities. Starting with open topological strings we work out the relation between the closed string sector dilaton tadpole, which appears in the annulus amplitude, and NSNS fluxes in the closed string dual on the resolved conifold. For the mirror closed string dual version on the deformed conifold we derive, for a non vanishing $G_{3}$ form, the $N$ supersymmetric vacua and the transformations of $G_{3}$ through domain walls. Finally, as an extension of Fischler Susskind mechanism we find a …
In string theory, there are various physical situations where the world-sheet fields have a shifted moding. For instance, this is the case for the twisted closed string in Z_N orbifold or for the charged open string in a constant electro-magnetic field. Because of this feature, it is quite challenging to give explicit formulae describing the string interaction, even for the bosonic case. In this note, we focus on the case of the charged open bosonic string and construct the 1-loop tadpole which is an object generating all 1-point functions from the annulus in the presence of an external field.…
We classify the possible bosonic and Type 0 unoriented string theories in two dimensions, and find their dual matrix(-vector) models. There are no RP^2 R-R tadpoles in any of the models, but many of them possess a massless tachyon tadpole. Thus all the models we find are consistent two-dimensional string vacua, but some get quantum corrections to their classical tachyon background. Where possible, we solve the tadpole cancellation condition, and find all the tachyon tadpole-free theories.
Tadpoles accompany, in one form or another, all attempts to realize supersymmetry breaking in String Theory, making the present constructions at best incomplete. Whereas these tadpoles are typically large, a closer look at the problem from a perturbative viewpoint has the potential of illuminating at least some of its qualitative features in String Theory. A possible scheme to this effect was proposed long ago by Fischler and Susskind, but incorporating background redefinitions in string amplitudes in a systematic fashion has long proved very difficult. In the first part of this paper, drawing…
We study the restrictions imposed by cancellation of the tadpoles for two, three, and four-form gauge fields in string theory, M-theory and F-theory compactified to two, three and four dimensions, respectively. For a large class of supersymmetric vacua, turning on a sufficient number of strings, membranes and three-branes, respectively, can cancel the tadpoles, and preserve supersymmetry. However, there are cases where the tadpole cannot be removed in this way, either because the tadpole is fractional, or because of its sign. For M-theory and F-theory compactifications, we also explore the rel…
We consider new objects in bosonic open string theory -- ND tadpoles, which have N(euman) boundary conditions at one end of the world-sheet and D(irichlet) at the other, must exist due to s-t duality in a string theory with both NN strings and D-branes. We demonstrate how to interpolate between N and D boundary conditions. In the case of mixed boundary conditions the action for a quantum particle is induced on the boundary. Quantum-mechanical particle-wave duality, a dual description of a quantum particle in either the coordinate or the momentum representation, is induced by world-sheet T-dual…
We discuss the role played by the divergences appearing in the interaction between a fractional D3 brane dressed with an SU(N) gauge field and a stack of N fractional D3 branes on the orbifolds C^2/Z_2 and C^3/(Z_2 x Z_2). In particular we show that the logarithmic divergences in the closed string channel, interpreted as due to twisted massless tadpoles, are mapped, under open/closed string duality, in the logarithmic ones in the open string channel, due to the massless states circulating in the annulus diagram and corresponding to the one-loop divergences that one finds in the gauge theory li…
We analyze the backreaction of dilaton tadpoles on the geometry of non-supersymmetric strings. After finding explicit warped solutions for a T-dual version of the Sugimoto model, we examine the possibility of realizing large extra dimension scenarios within the context of non-supersymmetric string models. Our analysis reveals an appealing mechanism to dynamically reduce the number of flat, non-compact directions in non-supersymmetric string theories.
We present several examples of T^8/P orbifolds with $P \subset SU(4)$. We compute their Hodge numbers and consider turning on discrete torsion. We then study supersymmetric compactifications of type II, heterotic, and type I strings on these orbifolds. Heterotic compactifications to D=2 have a B-field tadpole with coefficient given by that of the anomaly polynomial. In the SO(32) heterotic with standard embedding the tadpole is absent provided the internal space has a precise value of the Euler number. Guided by their relation to type I, we find tadpole-free SO(32) heterotic orbifolds with non…
Nonvanishing tadpoles and possible infinities associated in the multiparticle amplitudes are discussed with regard to the disk and $RP^{2}$ diagrams of the Type I' compactification. We find that the infinity cancellation of $SO(32)$ type $I$ theory extends to this case as well despite the presence of tadpoles localized in the D-brane world-volume and the orientifold surfaces. Formalism of string S-matrix generating functional is presented to find a consistent string background as c-number source function: we find this only treats the cancellation of the tadpoles in the linearized approximation…
Recent work has provided a direct string calculation of the internal coordinate dependence of gauge field tadpoles on the orbifold C^3/Z_3. We investigate the structure of these profiles in momentum and coordinate space representations using both analytical and numerical methods. The twisted states are determined to be localized within a few string lengths of the singularity. This provides an example of how delta-like singularities, which are typical for field theories on orbifolds, are avoided in string theory. A systematic expansion of the full string result allows us to speculate on how the…
We propose that perturbative quantum field theory and string theory can be consistently modified in the infrared to eliminate, in a radiatively stable manner, tadpole instabilities that arise after supersymmetry breaking. This is achieved by deforming the propagators of classically massless scalar fields and the graviton so as to cancel the contribution of their zero modes. In string theory, this modification of propagators is accomplished by perturbatively deforming the world-sheet action with bi-local operators similar to those that arise in double-trace deformations of AdS/CFT. This results…
We study RR charge cancellation consistency conditions in string compactifications with open string sectors, by introducing D-brane probes in the configuration. We show that uncancelled charges manifest as chiral gauge anomalies in the world-volume of suitable probes. RR tadpole cancellation can therefore be described as the consistency of the effective compactified theory not just in the vacuum, but also in all topological sectors (presence of D-brane probes). The result explains why tadpole cancellation is usually much stronger than anomaly cancellation of the compactified theory (in the vac…
We analyze non-supersymmetric four dimensional open string models of type IIB string theory compactified on $T^2\times K3$ with Scherk-Schwarz deformation acting on an $S^1$ of the $T^2$ torus. We find that there are always two solutions to the tadpole conditions that are shown to be connected via Wilson lines in an non-trivial way. These models although non-supersymmetric, are free of R-R and NS-NS tadpoles.
We study moduli stabilization for type IIB orientifold compactifications on Calabi-Yau three-folds with (non-)geometric fluxes. For this setting it is possible to stabilize all closed-string moduli classically without the need for non-perturbative contributions, and examples of stable de-Sitter constructions can be found in the literature which violate a prominent swampland conjecture. In this paper we derive general properties of non-geometric flux-compactifications, we argue that the contribution of fluxes to the tadpole cancellation conditions should be similar to D-branes (and not anti-D-b…
Certain classes of chiral four-dimensional gauge theories may be obtained as the worldvolume theories of D5-branes suspended between networks of NS5-branes, the so-called brane box models. In this paper, we derive the stringy consistency conditions placed on these models, and show that they are equivalent to anomaly cancellation of the gauge theories. We derive these conditions in the orbifold theories which are T-dual to the elliptic brane box models. Specifically, we show that the expression for tadpoles for unphysical twisted Ramond-Ramond 4-form fields in the orbifold theory are proportion…
We study orientifolds of type IIB string theory in the plane-wave background supported by null RR 3-form flux F^{(3)}. We describe how to extract the RR tadpoles in the Green-Schwarz formalism in a general setting. Two models with orientifold groups {1, Ω} and {1,ΩI_4}, which are T-dual to each other, are considered. Consistency of these backgrounds requires 32 D9 branes for the first model and 32 D5 branes for the second one. We study the spectra and comment on the heterotic duals of our models.
We discuss the interplay between IR and UV divergences in vacuum configurations with open and unoriented strings. We establish a general one-to-one correspondence between anomalies and R-R tadpoles associated to sectors with non-trivial Witten index. The result does not require any supersymmetry to be preserved by the configuration. Under very mild conditions of supersymmetry, a similar correspondence is found between NS-NS tadpoles and RG-flows in gauge theories on D-branes and O-planes. We briefly comment on the AdS/CFT counterpart of the results.
This is the first of a series of three papers on open string field theories based on Witten star product deformed with a gauge invariant open/closed coupling. This deformation is a tree-level tadpole which destabilizes the initial perturbative vacuum. We discuss the existence of vacuum-shift solutions which cancel the tadpole and represent a new configuration where the initial D-brane system has adapted to the change in the closed string background. As an example we consider the bulk deformation which changes the compactification radius and, to first order in the deformation, we reproduce the …
Aspects of strings without spacetime supersymmetry
Scuola Normale Superiore（高等师范学校）；INFN（意大利国家核物理研究所）；Instituto de Física Teórica IFT-UAM/CSIC（理论物理研究所 IFT-UAM/CSIC）；Universidad Autónoma de Madrid（马德里自治大学）
We investigate the properties of localized anomalous U(1)'s in heterotic string theory on the orbifold T^6/Z_3. We argue that the local four dimensional and original ten dimensional Green-Schwarz mechanisms can be implemented simultaneously, making the theory manifestly gauge invariant everywhere, in the bulk and at the fixed points. We compute the shape of the Fayet-Iliopoulos tadpoles, and cross check this derivation for the four dimensional auxiliary fields by a direct calculation of the tadpoles of the internal gauge fields. Finally we study some resulting consequences for spontaneous symm…
We use the Witten index in the open string sector to determine tadpole charges of orientifold planes and D-branes. As specific examples we consider type I compactifications on Calabi Yau manifolds and noncompact orbifolds. The tadpole constraints suggest that the standard embedding is not a natural choice for the gauge bundle. Rather there should be a close connection of the gauge bundle and the spin bundle. In the case of a four fold, the standard embedding does not in general fulfill the tadpole conditions. We show that this agrees with the Green-Schwarz mechanism. In the case of noncompact …
We derive a minimal set of Feynman rules for the loop amplitudes in unitary models of closed strings, whose target space is a simply laced (extended) Dynkin diagram. The string field Feynman graphs are composed of propagators, vertices (including tadpoles) of all topologies, and leg factors for the macroscopic loops. A vertex of given topology factorizes into a fusion coefficient for the matter fields and an intersection number associated with the corresponding punctured surface. As illustration we obtain explicit expressions for the genus-one tadpole and the genus-zero four-loop amplitude.
We review the emergence of the ten-dimensional fermionic closed string theories from subspaces of the Hilbert space of the 26-dimensional bosonic closed string theory compactified on an $E_8\times SO(16)$ lattice. They arise from a consistent truncation procedure which generates space-time fermions out of bosons. This procedure is extended to open string sectors. We prove, from bosonic considerations alone, that truncation of the unique tadpole-free $SO(2^{13})$ bosonic string theory compactified on the above lattice determines the anomaly free Chan-Paton group of the Type I theory. It also yi…
We investigate the effects of the leading tadpole potentials of 10D tachyon-free non-supersymmetric strings in warped products of flat geometries of the type M(p+1) x R x T(10-p-2) depending on a single coordinate. In the absence of fluxes and for p<8, there are two families of these vacua for the orientifold disk-level potential, both involving a finite internal interval. Their asymptotics are surprisingly captured by tadpole-free solutions, isotropic for one family and anisotropic at one end for the other. In contrast, for the heterotic torus-level potential there are four types of vacua. Th…
We examine the ghost contribution to the one-loop integrands in open string field theory using the Moyal representation of the star product. We primarily focus on the open string tadpole integrand, which is an intrinsically off-shell quantity. Due to the closed string tachyon, the full amplitude is badly divergent from the closed string degeneration region $t\to0^+$ of the Schwinger parameter. We obtain expansions for the finite factors from the squeezed state matrix ${\bf R}(t)$ characterizing the ghost part of the tadpole in Siegel gauge. The analytic structure of the integrands, as a functi…
We study the Fayet-Iliopoulos (FI) D-terms on D-branes in type II Calabi-Yau backgrounds. We provide a simple worldsheet proof of the fact that, at tree level, these terms only couple to scalars in closed string hypermultiplets. At the one-loop level, the D-terms get corrections only if the gauge group has an anomalous spectrum, with the anomaly cancelled by a Green-Schwarz mechanism. We study the local type IIA model of D6-branes at SU(3) angles and show that, as in field theory, the one-loop correction suffers from a quadratic divergence in the open string channel. By studying the closed str…
We construct the Hamiltonian operator of the string field theory for $c=0$ string theory. It describes how strings evolve in the coordinate frame, which is defined by using the geodesic distance on the worldsheet. The Hamiltonian consists of three-string interaction terms and a tadpole term. We show that one can derive the loop amplitudes of $c=0$ string theory from this Hamiltonian.
We study generic properties of string theory effective actions obtained by classically integrating out massive excitations from string field theories based on cyclic homotopy algebras of $A_\infty$ or $L_\infty$ type. We construct observables in the UV theory and we discuss their fate after integration-out. Furthermore, we discuss how to compose two subsequent integrations of degrees of freedom (horizontal composition) and how to integrate out degrees of freedom after deforming the UV theory with a new consistent interaction (vertical decomposition). We then apply our general results to the op…
We compute the one loop partition function of type IIB string in plane wave R-R 5-form background $F^5$ using both path integral and operator formalisms and show that the two results agree perfectly. The result turns out to be equal to the partition function in the flat background. We also study the Tadpole cancellation for the unoriented closed and open string model in plane wave R-R 5-form background studied in hep-th/0203249 and find that the cancellation of the Tadpole requires the gauge group to be SO(8).
We demonstrate that an Erler-Schnabl type solution in cubic string field theory can be naturally interpreted as a gauge invariant regularization of an identity based solution. We consider a solution which interpolates between an identity based solution and ordinary Erler-Schnabl one. Two gauge invariant quantities, the classical action and the closed string tadpole, are evaluated for finite value of the gauge parameter. It is explicitly checked that both of them are independent of the gauge parameter.
The possibility of radiative gauge symmetry breaking on D3-branes at non-supersymmetric orbifold singularities is examined. As an example, a simple model of D3-branes at non-supersymmetric C^3/Z_6 singularity with some D7-branes for the cancellations of R-R tadpoles in twisted sectors is analyzed in detail. We find that there are no tachyon modes in twisted sectors, and NS-NS tadpoles in twisted sectors are canceled out, though uncanceled tadpoles and tachyon modes exist in untwisted sectors. This means that this singularity background is a stable solution of string theory at tree level, thoug…
We apply the replica trick to compute the entropy of a cylinder amplitude in string theory. We focus on the contribution from non-perturbative winding modes and impose tadpole cancellation to understand the correct prescription for integrating over moduli. Choosing the entangling surface to cut longitudinally over the whole length of the cylinder, we obtain an answer that is interpreted as the entropy of a density matrix. We recast this result in target space language, both in the open and closed string picture.
We review the main results of our investigations motivated by the tadpole potentials of ten-dimensional strings with broken supersymmetry. While these are at best partial indications, it is hard to resist the feeling that they do capture some lessons of String Theory. For example, these very tadpole potentials lead to weak-string-coupling cosmologies that appear to provide clues on the onset of the inflation from an initial fast roll. The transition, if accessible to us, would offer a natural explanation for the lack of power manifested by the CMB at large angular scales. In addition, the same…
We discuss the interpaly between IR and UV divergences in theories with open and unoriented strings in view of the AdS/CFT correspondence. We start by deriving general formulas for the computation of threshold corrections to gauge couplings in generic configurations with open and unoriented strings. These allow us to discuss the IR/UV correspondence between beta-function coefficients and ``dilaton'' tadpoles for several brane configurations probed by D3-branes. Finally we comment on the AdS supergravity descriptions of gauge theories that are (super)conformal in the large N limit.
We study how the effect of closed-string tachyon condensation can enter into the on-shell effective action of open-string tachyons in the bosonic case. We also consider open-string one-loop quantum corrections to the on-shell action. We use a sigma-model approach with boundary terms, and we utilize some results of boundary string field theory (BSFT) to define the on-shell effective action. We regard D-instanton-like objects with appropriate weight as closed-string tachyon tadpoles, and we insert them into worldsheets to analyze the effect of closed-string tachyons.
In light of Sen's weak coupling limit of F-theory as a type IIB orientifold, the compatibility of the tadpole conditions leads to a non-trivial identity relating the Euler characteristics of an elliptically fibered Calabi-Yau fourfold and of certain related surfaces. We present the physical argument leading to the identity, and a mathematical derivation of a Chern class identity which confirms it, after taking into account singularities of the relevant loci. This identity of Chern classes holds in arbitrary dimension, and for varieties that are not necessarily Calabi-Yau. Singularities are ess…
We review some of the features of Type IIA compactifications in the presence of fluxes. In particular, the case of $T^6/(Ω(-1)^{F_L} σ)$ orientifolds with RR, NS and metric fluxes is considered. This has revealed to possess remarkable properties such as vacua with all the closed string moduli stabilized, null or negative contributions to the RR tadpoles or supersymmetry on the branes enforced by the closed string background. In this way, Type IIA compactifications with non trivial fluxes seem to constitute a new window into the building of semi-realistic models in String Theory.
We study gauge threshold corrections for local brane models embedded in a large compact space. A large bulk volume gives important contributions to the Konishi and super-Weyl anomalies and the effective field theory analysis implies the unification scale should be enhanced in a model-independent way from M_s to R M_s. For local D3/D3 models this result is supported by the explicit string computations. In this case the scale R M_s comes from the necessity of global cancellation of RR tadpoles sourced by the local model. We also study D3/D7 models and discuss discrepancies with the effective fie…
We study gauge threshold corrections for local GUT models in IIB/F-theory. Consistency with holomorphy requirements of supergravity and the Kaplunovsky-Louis formula implies that the unification scale is enhanced by the bulk radius R from the string scale to M_X =RM_S. We argue that the stringy interpretation of this is via a locally uncancelled tadpole sourced by the hypercharge flux. This sources closed string modes propagating into the bulk; equivalently open string gauge coupling running up to the winding scale M_X. The enhancement to R M_s is tied to GUT breaking by a globally trivial hyp…
In the presence of internal magnetic fields, a D9 brane can acquire a D5 (or anti-D5) R-R charge, and can therefore contribute to the corresponding tadpole. In the resulting vacua, supersymmetry is generically broken and tachyonic instabilities are present. However, suitable choices for the magnetic fields, corresponding to self-dual configurations in the internal space, can yield new chiral supersymmetric vacua with gauge groups of reduced rank, where the magnetic energy saturates, partly or fully, the negative tension of the O5+ planes. These models contain Green-Schwarz couplings to untwist…
We study the physics of D-branes in the presence of constant Ramond-Ramond potentials. In the string field theory context, we first develop a general formalism to analyze open strings in gauge trivial closed string backgrounds, and then apply it both to the RNS string and within Berkovits' covariant formalism, where the results have the most natural interpretation. The most remarkable finding is that, in the presence of a Dp-brane, both a constant parallel NS-NS B-field and R-R C^(p-1)-field do not solve the open/closed equations of motion, and induce the same non-vanishing open string tadpole…
In this thesis we provide new tools to determine and explore the Landscape of four-dimensional effective field theories originating from string and M-theory. The main aim is to introduce, within four-dimensional effective descriptions, elements that are predicted from string theory. To this end, a hierarchy of forms is introduced within the four-dimensional $\mathcal{N}=1$ supergravity theories. The inclusion of gauge three-forms delivers a dynamical way to generate flux-induced superpotentials. Instead, gauge two-forms, dual descriptions of axions, may be eventually gauged by three-forms to g…
We study the stabilization of all closed string moduli in the T^6/Z_2 orientifold, using constant internal magnetic fields and 3-form fluxes that preserve N=1 supersymmetry in four dimensions. We first analyze the stabilization of Kahler class and complex structure moduli by turning on magnetic fluxes on different sets of D9 branes that wrap the internal space T^6/Z_2. We present explicit consistent string constructions, satisfying in particular tadpole cancellation, where the radii can take arbitrarily large values by tuning the winding numbers appropriately. We then show that the dilaton-axi…
Light-front gauge is the most popular one to work with fundamental interactions, due to its characteristic maximum kinematical Poincare operators that it allows. However, it is also known to be one of the trickiest gauges one can work with for gauge theories, due to its singular nature. So, in terms of perturbative calculations in the light-front, there are only a few published and tabulated results for the pertinent Feynman integrals, mostly involving massless integrals. And the majority of the results given are only for the divergent parts of them and the complete closed form (or with the fi…
