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Register a new userOperator Formulation of Green-Schwarz Superstring in the Semi-Light-Cone Conformal Gauge
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In this article we present a comprehensive account of the operator formulation of the Green-Schwarz superstring in the semi-light-cone (SLC) gauge, where the worldsheet conformal invariance is preserved. Starting from the basic action, we systematically study the symmetry structure of the theory in the SLC gauge both in the Lagrangian and the phase space formulations. After quantizing the theory in the latter formulation we construct the quantum Virasoro and the super-Poincare generators and clarify the closure properties of these symmetry algebras. Then by making full use of this knowledge we will be able to construct the BRST-invariant vertex operators which describe the emission and the absorption of the massless quanta and show that they form the appropriate representation of the quantum symmetry algebras. Furthermore, we will construct an exact quantum similarity transformation which connects the SLC gauge and the familiar light-cone (LC) gauge. As an application BRST-invariant DDF operators in the SLC gauge are obtained starting from the corresponding physical oscillators in the LC gauge.
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We consider possible discretizations for a gauge-fixed Green-Schwarz action of Type IIB superstring. We use them for measuring the action, from which we extract the cusp anomalous dimension of planar $mathcal{N}=4$ SYM as derived from AdS/CFT, as well as the mass of the two $AdS$ excitations transverse to the relevant null cusp classical string solution. We perform lattice simulations employing a Rational Hybrid Monte Carlo (RHMC) algorithm and two Wilson-like fermion discretizations, one of which preserves the global $SO(6)$ symmetry of the model. We compare our results with the expected behavior at various values of $g=frac{sqrt{lambda}}{4pi}$. For both the observables, we find a good agreement for large $g$, which is the perturbative regime of the sigma-model. For smaller values of $g$, the expectation value of the action exhibits a deviation compatible with the presence of quadratic divergences. After their non-perturbative subtraction the continuum limit can be taken, and suggests a qualitative agreement with the non-perturbative expectation from AdS/CFT. Furthermore, we detect a phase in the fermion determinant, whose origin we explain, that for very small $g$ leads to a sign problem not treatable via standard reweigthing. The continuum extrapolations of the observables in the two different discretizations agree within errors, which is strongly suggesting that they lead to the same continuum limit. Part of the results discussed here were presented earlier in arXiv:1601.04670.
We construct a world-sheet action for Green-Schwarz superstring in terms of doubled-yet-gauged spacetime coordinates. For an arbitrarily curved NS-NS background, the action possesses $mathbf{O}(10,10)$ T-duality, $mathbf{Spin}(1,9)timesmathbf{Spin}(9,1)$ Lorentz symmetry, coordinate gauge symmetry, spacetime doubled-yet-gauged diffeomorphisms, world-sheet diffeomorphisms and Weyl symmetry. Further, restricted to flat backgrounds, it enjoys maximal spacetime supersymmetry and kappa-symmetry. After the auxiliary coordinate gauge symmetry potential being integrated out, our action can consistently reduce to the original undoubled Green-Schwarz action. Thanks to the twofold spin groups, the action is unique: it is specific choices of the NS-NS backgrounds that distinguish IIA or IIB, as well as lead to non-Riemannian or non-relativistic superstring a la Gomis-Ooguri which might deserve the nomenclature, type IIC.
We propose a dimensional regularization scheme to deal with the divergences caused by colliding supercurrents inserted at the interaction points, in the light-cone gauge NSR superstring field theory. We formulate the theory in $d$ dimensions and define the amplitudes as analytic functions of $d$. With an appropriately chosen three-string interaction term and large negative $d$, the tree level amplitudes for the (NS,NS) closed strings can be recast into a BRST invariant form, using the superconformal field theory proposed in Ref.[arXiv:0911.3704]. We show that in the limit $d to 10$ they coincide with the results of the first quantized theory. Therefore we obtain the desired results without adding any contact interaction terms to the action.
We reconsider the analysis done by Kazama and Yokoi in arXiv:0801.1561 (hep-th). We find that although the right vacuum of the theory is the one associated to massless normal ordering (MNO), phase space normal ordering (PNO) plays crucial role in the analysis in the following way. While defining the quantum energy-momentum (EM) tensor one needs to take into account the field redefinition relating the space-time field and the corresponding world-sheet coupling. We argue that for a simple off-shell ansatz for the background this field redefinition can be taken to be identity if the interaction term is ordered according to PNO. This definition reproduces the correct physical spectrum when the background is on-shell. We further show that the right way to extract the effective equation of motion from the Virasoro anomaly is to first order the anomaly terms according to PNO at a finite regularization parameter $eps$ and then take the $eps to 0$ limit. This prescription fixes an ambiguity in taking the limit for certain bosonic and fermionic contributions to the Virasoro anomaly and is the natural one to consider given the above definition of the EM tensor.
We consider the dimensional regularization of the light-cone gauge type II superstring field theories in the NSR formalism. In the previous work, we have calculated the tree-level amplitudes with external lines in the (NS,NS) sector using the regularization and shown that the desired results are obtained without introducing contact term interactions. In this work, we study the tree-level amplitudes with external lines in the Ramond sector. In order to deal with them, we propose a worldsheet theory to be used instead of that for the naive dimensional regularization. With the worldsheet theory, we regularize and define the tree-level amplitudes by analytic continuation. We show that the results coincide with those of the first quantized formulation.
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