Superstring Research Articles

Energy quantization for a nonlinear sigma model with critical gravitinos

We study some analytical and geometric properties of a two-dimensional nonlinear sigma model with gravitino which comes from supersymmetric string theory. When the action is critical w.r.t. variations of the various fields including the gravitino, there is a symmetric, traceless, and divergence-free energy-momentum tensor, which gives rise to a holomorphic quadratic differential. Using it we obtain a Pohozaev type identity and finally we can establish the energy identities along a weakly convergent sequence of fields with uniformly bounded energies.

Sketching a proof of the Maldacena conjecture at small radius

At small AdS radius, the superstring on AdS5 × S5 was conjectured by Maldacena to be equivalent to mathcal{N} = 4 super-Yang-Mills at small ‘t Hooft coupling where thickened Feynman diagrams can be used to compute scattering amplitudes. It was previously shown that the pure spinor worldsheet action of the AdS5 × S5 superstring can be expressed as the sum of a BRST-trivial term and a “B-term” which is antisymmetric in worldsheet derivatives. Using the explicit form of the pure spinor vertex operators, it will be argued here that the free super-Yang-Mills Feynman diagrams are described by the BRST-trivial term where the thickened propagators are the regions of the string worldsheet near the AdS boundary and the holes are the regions near the AdS horizon. Evidence will then be presented that the antisymmetric B-term generates the super-Yang-Mills vertex so that, at small radius and arbitrary genus, the superstring amplitudes correctly reproduce the super-Yang-Mills Feynman diagram expansion.

All order α′ corrections to fermionic couplings of D-brane-Anti-D-brane effective actions

We first point out to all order α′ corrections to lower order fermionic couplings and their effective actions of type II super string theory. In order to reveal all symmetries of the particular D-brane Anti-D-brane system, and to construct not only all the singularity structures but also all order α′ corrections of fermionic couplings to tachyons, we employ all the Conformal Field Theory (CFT) methods to a six point function. Basically, we construct all the correlation functions of four spin operators and two world sheet fermion fields. The S-matrix of two fermion fields, two real tachyons in the presence of a closed string Ramond-Ramond (RR) field in type II will be explored. Applying all the symmetries of the amplitude, a proper expansion for D-brane Anti D-brane is also found out. Having carried out all the Effective Field Theory (EFT) techniques, one would discover all order singularity structures of string theory. The entire algebraic computations of the amplitude of <VC−1(z,z̄) Vψ̄−1/2(x1) Vψ−1/2(x2) VT0(x3) VT0(x4)> have also been derived. Various new string couplings are revealed as well. Eventually, making comparison the S-matrix with all EFT parts, all order α′ higher derivative corrections to two fermions- two tachyons in the world volume of D-brane Anti D-brane of type II are discovered accordingly.

Leading higher-derivative corrections to Kerr geometry

We compute the most general leading-order correction to Kerr solution when the Einstein-Hilbert action is supplemented with higher-derivative terms, including the possibility of dynamical couplings controlled by scalars. The model we present depends on five parameters and it contains, as particular cases, Einstein-dilaton-Gauss-Bonnet gravity, dynamical Chern-Simons gravity and the effective action coming from Heterotic Superstring theory. By solving the corrected field equations, we find the modified Kerr metric that describes rotating black holes in these theories. We express the solution as a series in the spin parameter χ, and we show that including enough terms in the expansion we are able to describe black holes with large spin. For the computations in the text we use an expansion up to order χ14, which is accurate for χ < 0.7, but we provide as well a Mathematica notebook that computes the solution at any given order. We study several properties of the corrected black holes, such as geometry of the horizon, ergosphere, light rings and scalar hair. Some of the corrections violate parity, and we highlight in those cases plots of horizons and ergospheres without ℤ2 symmetry.

The worldsheet dual of the symmetric product CFT

Superstring theory on {mathrm{AdS}}_3 times {S}^3times {mathbb{T}}^4 with the smallest amount of NS-NS flux (“k = 1”) is shown to be dual to the spacetime CFT given by the large N limit of the free symmetric product orbifold SymN left({mathbb{T}}^4right) . To define the worldsheet theory at k = 1, we employ the hybrid formalism in which the AdS3 × S3 part is described by the mathfrak{p}mathfrak{s}mathfrak{u}{left(1,1Big|2right)}_1 WZW model (which is well defined). Unlike the case for k ≥ 2, it turns out that the string spectrum at k = 1 does not exhibit the long string continuum, and perfectly matches with the large N limit of the symmetric product. We also demonstrate that the fusion rules of the symmetric orbifold are reproduced from the worldsheet perspective. Our proposal therefore affords a tractable worldsheet description of a tensionless limit in string theory, for which the dual CFT is also explicitly known.

Reliability Analysis of Super 13Cr Tubing in Ultra-Deep Gas Well

Abnormal oil casing pressure appeared in the process of test production of multiple Ultra-Deep Gas Wells in Tarim Basin. The super 13Cr oil pipe string was used to analyze the causes of pipe string failure in view of the oil casing channeling well during the test and blowout period. The construction process of the well was analyzed in detail. Combined with the review of the operation flow and the detection of fracture string material and fracture morphology, the causes of pipe string fracture were analyzed and calculated in detail. Through field investigation, analysis and calculation, it was found that the main cause of cracking of super 13Cr tubing in this well is the decrease of vibration natural frequency caused by excessive fluid velocity in pipe and too long span of pipe string. At the same time, the mixed failure of stress corrosion cracking and stress load interaction occurred in Cl−1 environment and other corrosion environments.

THE SUPERSTRING THEORY AND THE SHAPE OF PROTONS AND ELECTRONS

According to “Superstring Theory”, the electron and proton are made of similar tiny supersymmetric strings (Gefter, 2007; Green, Schwarz, &amp; Witten, 2012; Schwarz, 1982; Sharma, 2010). In this paper we introduce a sample particle that is such tiny supersymmetric string or made of it and also we use scientific achievements of experiments about electron and proton specifications to verify and compare the electron and proton dimensions and masses with this sample. By using logical reasons, we reject one of the methods of measuring of electrons’ radius. Finally, using simple mathematical formulas, we prove that although the electrons and protons are both spherical, but one is hollow and the other is dense .

Exploring the existence of extra dimension(s)

Whether there exists extra dimensions is an interesting and fundamental question. In this article, certain aspects of this have been explored theoretically. For this purpose, we first discuss the role of an extra dimension in the early unification of the classical Einstein gravity and electromagnetic interaction, namely the Kaluza-Klein (KK-) theory, and the issues we encounter in carrying this out. We then move to discuss the relationship between supersymmetry and extra dimension(s) and point out that there exist well-defined quantum theories without gravity in six dimensions such as (2, 0) superconformal theory and little string theories, the former is a local field theory but has no Lagrangian description while the latter are non-local non-gravitational string theories. We discuss also the similar issue for supergravities in diverse dimensions and point out that the largest number of supersymmetries with propagating gravity degrees of freedom is $N$=8 in four dimensions and the largest number of spacetime dimensions for supergravity is eleven. We would like to stress that extra dimensions in classical supersymmetric theories such as supergravities in diverse dimensions appear only as an option. When gravity is included, the four-dimensional $N$=8 supergravity appears to be the only one so far which has the potential to be a good quantum gravity theory in the usual field theory sense. All the rest are sure to be UV incomplete ones whose UV completions require the existence of an unified theory which is most likely to be the string/M-theory. In this sense, a quantum consistent theory containing gravity needs extra dimensions in general. Good examples include both bosonic strings and superstrings. For the former, we need the spacetime dimensions to be twenty six while for the latter we need spacetime dimensions to be ten such that the corresponding theories are quantum consistent at least perturbatively. So for these quantum consistent theories containing gravity, extra dimensions are no longer optional but must be there. In this paper, we give also an elementary introduction to both bosonic string and superstring theories. We mention that in addition to the usual one dimensional strings, there exist also non-perturbative $p$-branes with $p~=~0,~1,~\cdots~9$ in non-perturbative superstring theories. These $p$-branes are the so-called 1/2 BPS extended objects, preserving one half of the spacetime supersymmetries. They play the key role in establishing various dualities such as S-duality and U-duality and help to explain how the existence of various superstring theories leads to that of an even bigger unified theory called M-theory, which unifies 5 superstrings in ten dimensions and the 11-dimensional supergravity, with its largest spacetime dimension to be eleven. To bring the string/M-theory to our four-dimensional real world, we usually need to compactify six or seven extra dimensions, which should be small enough to avoid experimental constraints. Phenomenologically, people also explore the existence of large extra dimensions, which can be used to solve gauge hierarchy problem or gravity localization, etc. We give some discussions on these topics as well.

Entanglement entropy for open bosonic strings on Dp-branes

We study the entanglement entropy for open bosonic strings on multiple Dp-branes by using the covariant open string field theory. Choosing one of the spatial coordinates which are tangential to the hyperplane on which Dp-branes are located, we divide the hyperplane into two halves. By using the string wavefunction in the Fock space representation, we evaluate the entanglement entropy. The entanglement entropy is found to be proportional to the area of (p−1)-dimensional boundary of the bipartite hyperplanes and divergent in the ultraviolet (UV) region as well as in the infrared (IR) region. However, the leading divergences are mainly due to tachyon contributions to the entanglement entropy, which may be absent in supersymmetric string theories. Apart from the divergences thanks to tachyons, the entanglement entropy for open bosonic strings on Dp-branes is finite for 2≤p≤dcritical−2 and logarithmically divergent for p=1,dcritical−1.

Local \u03b2-deformations and Yang-Baxter sigma model

Homogeneous Yang-Baxter (YB) deformation of AdS5 × S5 superstring is revisited. We calculate the YB sigma model action up to quadratic order in fermions and show that homogeneous YB deformations are equivalent to β-deformations of the AdS5 ×S5 background when the classical r-matrices consist of bosonic generators. In order to make our discussion clearer, we discuss YB deformations in terms of the double-vielbein formalism of double field theory. We further provide an O(10, 10)-invariant string action that reproduces the Green-Schwarz type II superstring action up to quadratic order in fermions. When an AdS background contains a non-vanishing H-flux, it is not straightforward to perform homogeneous YB deformations. In order to get any hint for such YB deformations, we study β-deformations of H-fluxed AdS backgrounds and obtain various solutions of (generalized) type II supergravity.

On the dynamics of superstring compactification

Compactification of the ten-dimensional heterotic superstring theory to four dimensions gives rise to two moduli potentials $V_{A}$ , $V_{B}$ , the positive semi-definiteness of which places constraints on the Euler characteristic $ \bar{\chi}$ of the internal space $\bar{g}_{\mu\nu}(y^{\xi})$ and the adiabatic index $\gamma$ of the effective matter source of energy-density $\rho$ and pressure $p = (\gamma -1)\rho$ that generates the physical four-space $g_{ij}(x^{k})$ , namely $\bar{\chi} < 0$ , $4/3 \leq \gamma \leq 2$ , or $\bar{\chi} > 0$ , $1 \leq \gamma \leq 4/3$ . Here, we show how fermion-bilinear condensation in the internal space, first put forward by Helayel-Neto and Smith, determines the field $\tilde{\beta} \equiv A_{\rm r} B_{\rm r}^{3}$ , thus reducing the moduli space to a single canonical field $\tilde{\sigma}=2\sigma_{B}$ with a potential ˜ , which is positive semi-definite under the same conditions that ensure positive semi-definiteness of $V_{A}$ , $V_{B}$ , and has a minimum at a value of $\tilde{\beta}$ that is approximately constant far from the Planck era at $t \gg t_{\rm P}$ . The fields $\sigma_{A}$ , $\sigma_{B}$ , which are canonically normalized in the zero-slope limit, are modified by contributions originating from the higher-derivative gravitational terms $\alpha^{\prime} \hat{\mathcal{R}}_{\rm E}^{2}$ and $\alpha^{\prime 3} \hat{\mathcal{R}}^{4}$ , but the associated kinetic energy remains positive for times $t \gtrsim t_{\rm P}/2$ , guaranteeing classical stability of the solution, since the generalized indeterminacy principle implies a minimum physically measurable time $t_{0} \approx 50 t_{\rm P}$ for the superstring theory.

On non-BPS effective actions of string theory

We discuss some physical prospective of the non-BPS effective actions of type IIA and IIB superstring theories. By dealing with all complete three and four point functions, including a closed Ramond–Ramond string (in terms of both its field strength and its potential), gauge (scalar) fields as well as a real tachyon and under symmetry structures, we find various restricted world volume and bulk Bianchi identities. The complete forms of the non-BPS scattering amplitudes including their Chan–Paton factors are elaborated. All the singularity structures of the non-BPS amplitudes, their all order alpha ' higher-derivative corrections, their contact terms and various modified Bianchi identities are derived. Finally, we show that scattering amplitudes computed in different super-ghost pictures are compatible when suitable Bianchi identities are imposed on the Ramond–Ramond fields. Moreover, we argue that the higher-derivative expansion in powers of the momenta of the tachyon is universal.

On the exactness of soft theorems

Soft behaviours of S-matrix for massless theories reflect the underlying symmetry principle that enforces its masslessness. As an expansion in soft momenta, sub-leading soft theorems can arise either due to (I) unique structure of the fundamental vertex or (II) presence of enhanced broken-symmetries. While the former is expected to be modified by infrared or ultraviolet divergences, the latter should remain exact to all orders in perturbation theory. Using current algebra, we clarify such distinction for spontaneously broken (super) Poincaré and (super) conformal symmetry. We compute the UV divergences of DBI, conformal DBI, and A-V theory to verify the exactness of type (II) soft theorems, while type (I) are shown to be broken and the soft-modifying higher-dimensional operators are identified. As further evidence for the exactness of type (II) soft theorems, we consider the α′ expansion of both super and bosonic open strings amplitudes, and verify the validity of the translation symmetry breaking soft-theorems up to mathcal{O}left({alpha}^{prime 6}right) . Thus the massless S-matrix of string theory “knows” about the presence of D-branes.

Poisson-Lie duals of the \u03b7 deformed symmetric space sigma model

Poisson-Lie dualising the η deformation of the G/H symmetric space sigma model with respect to the simple Lie group G is conjectured to give an analytic continuation of the associated λ deformed model. In this paper we investigate when the η deformed model can be dualised with respect to a subgroup G0 of G. Starting from the first-order action on the complexified group and integrating out the degrees of freedom associated to different subalgebras, we find it is possible to dualise when G0 is associated to a sub-Dynkin diagram. Additional U1 factors built from the remaining Cartan generators can also be included. The resulting construction unifies both the Poisson-Lie dual with respect to G and the complete abelian dual of the η deformation in a single framework, with the integrated algebras unimodular in both cases. We speculate that extending these results to the path integral formalism may provide an explanation for why the η deformed AdS5 × S5 superstring is not one-loop Weyl invariant, that is the couplings do not solve the equations of type IIB supergravity, yet its complete abelian dual and the λ deformed model are.

Quantum spectral curve for the η-deformed AdS5 × S5 superstring

The spectral problem for the AdS5×S5 superstring and its dual planar maximally supersymmetric Yang–Mills theory can be efficiently solved through a set of functional equations known as the quantum spectral curve. We discuss how the same concepts apply to the η-deformed AdS5×S5 superstring, an integrable deformation of the AdS5×S5 superstring with quantum group symmetry. This model can be viewed as a trigonometric version of the AdS5×S5 superstring, like the relation between the XXZ and XXX spin chains, or the sausage and the S2 sigma models for instance. We derive the quantum spectral curve for the η-deformed string by reformulating the corresponding ground-state thermodynamic Bethe ansatz equations as an analytic Y system, and map this to an analytic T system which upon suitable gauge fixing leads to a Pμ system – the quantum spectral curve. We then discuss constraints on the asymptotics of this system to single out particular excited states. At the spectral level the η-deformed string and its quantum spectral curve interpolate between the AdS5×S5 superstring and a superstring on “mirror” AdS5×S5, reflecting a more general relationship between the spectral and thermodynamic data of the η-deformed string. In particular, the spectral problem of the mirror AdS5×S5 string, and the thermodynamics of the undeformed AdS5×S5 string, are described by a second rational limit of our trigonometric quantum spectral curve, distinct from the regular undeformed limit.

Gravitational perfect fluid collapse in Gauss\u2013Bonnet gravity

The Einstein Gauss–Bonnet theory of gravity is the low-energy limit of heterotic super-symmetric string theory. This paper deals with gravitational collapse of a perfect fluid in Einstein–Gauss–Bonnet gravity by considering the Lemaitre–Tolman–Bondi metric. For this purpose, the closed form of the exact solution of the equations of motion has been determined by using the conservation of the stress-energy tensor and the condition of marginally bound shells. It has been investigated that the presence of a Gauss–Bonnet coupling term alpha >0 and the pressure of the fluid modifies the structure and time formation of singularity. In this analysis a singularity forms earlier than a horizon, so the end state of the collapse is a naked singularity depending on the initial data. But this singularity is weak and timelike, which goes against the investigation of general relativity.

Remarks on non-BPS string amplitudes and their all order \u03b1\u2032 contact interactions in IIB, IIA

We explore the entire form of S-Matrix elements of a potential Cn−1 Ramond-Ramond (RR) form field, a tachyon and two transverse scalar fields on both world volume and transverse directions of type IIB and IIA superstring theories. Apart from leftlangle {V}_{C^{-2}}{V}_{phi^0}{V}_{phi^0}{V}_{T^0}rightrangle the other scattering amplitude, namely leftlangle {V}_{C^{-1}}{V}_{phi^{-1}}{V}_{phi^0}{V}_{T^0}rightrangle is also revealed. We then start to compare all singularity structures of symmetric and asymmetric analysis, generating all infinite singularity structures as well as all order α′ contact interactions on the whole directions. This leads to deriving various new contact terms and several new restricted Bianchi identities in both type IIB and IIA. It is also shown that just some of the new couplings of type IIB (IIA) string theory can be re-verified in an Effective Field Theory (EFT) by pull-back of branes. To construct the rest of S-matrix elements one needs to first derive restricted world volume (or bulk) Bianchi identities and then discover new EFT couplings in both type IIB and IIA. Finally the presence of commutator of scalar fields inside the exponential of Wess-Zumino action for non-BPS branes has been confirmed as well.

Resurgence of the dressing phase for AdS5 \xd7 S5

We discuss the resummation of the strong coupling asymptotic expansion of the dressing phase of the AdS5 × S5 superstring. The dressing phase proposed by Beisert, Eden and Staudacher can be recovered from a modified Borel-Ecalle resummation of this asymptotic expansion only by completing it with new, non-perturbative and exponentially suppressed terms that can be organized into different sectors labelled by an instanton-like number. We compute the contribution to the dressing phase coming from the sum over all the instanton sectors and show that it satisfies the homogeneous crossing symmetry equation. We comment on the semiclassical origin of the non-perturbative terms from the world-sheet theory point of view even though their precise explanation remains still quite mysterious.

Cosmological solutions in low-energy effective field theory for type IIA superstrings

It is known that to obtain cosmological solutions consistent with the Hubble law and accelerated expansion, it is necessary to represent space-time in the form of de Sitter space of the first kind, which ismost simply described by a Robertson-Walkermetric having the scale factor with exponential time dependence. In standard general relativity, this solution is obtained by introduction of the cosmological constant Λ associated with dark energy, whose nature is still not clear. It would be of some interest to consider theories allowing one to obtain cosmological-type solutions without using an effective Λ term. This role was at their time claimed by various supergravity theories which are low-energy approximations of superstring theories. However, it was found that in these theories there are so-called no-go theorems which do not allow solutions in the form of de Sitter space of the first kind. It turned out that this problem can be solved in at least two ways. The first way is to admit the possibility of extra time dimensions, as was demonstrated for the ten-dimensional supergravity by Arefyeva et al. Another way is to consider corrections of higher order in the curvature tensor, which is a subject of this paper. As is known, non-chiral ten-dimensional N = 2 supergravity is a low-energy approximation of type IIA superstring theory. In the present paper, we consider the effective action for type IIA superstring theory, taking into account fourthorder curvature corrections. It is shown that in this case, indeed, one can obtain a cosmological solution in the form of de Sitter space, describing an exponential expansion of space without an effective Λ term.

Physics of the Mind.

Is it possible to turn psychology into “hard science”? Physics of the mind follows the fundamental methodology of physics in all areas where physics have been developed. What is common among Newtonian mechanics, statistical physics, quantum physics, thermodynamics, theory of relativity, astrophysics… and a theory of superstrings? The common among all areas of physics is a methodology of physics discussed in the first few lines of the paper. Is physics of the mind possible? Is it possible to describe the mind based on the few first principles as physics does? The mind with its variabilities and uncertainties, the mind from perception and elementary cognition to emotions and abstract ideas, to high cognition. Is it possible to turn psychology and neuroscience into “hard” sciences? The paper discusses established first principles of the mind, their mathematical formulations, and a mathematical model of the mind derived from these first principles, mechanisms of concepts, emotions, instincts, behavior, language, cognition, intuitions, conscious and unconscious, abilities for symbols, functions of the beautiful and musical emotions in cognition and evolution. Some of the theoretical predictions have been experimentally confirmed. This research won national and international awards. In addition to summarizing existing results the paper describes new development theoretical and experimental. The paper discusses unsolved theoretical problems as well as experimental challenges for future research.