Marco Baumgartl, Ivo Sachs
We address the problem of describing different closed string backgrounds in background independent open string field theory: A shift in the closed string background corresponds to a collective excitation of open strings. As an illustration we apply the formalism to the case where the closed string background is a group manifold.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We present a string theory realization for the correspondence between quantum integrable models and supersymmetric gauge theories. The quantization results from summing the effects of fundamental strings winding around a compact direction. We discuss the examples of the XXZ gauge/Bethe correspondence and five-dimensional Ω--deformed SYM on M x S^1.
In a recent essay, we discussed the possibility of using polymer sizing to model the collapse of a single, long excited string to a black hole. In this letter, we apply this idea to bring further support to string/black hole correspondence. In particular, we reproduce Horowitz and Polchinki's results for self-gravitating fundamental strings and speculate on the nature of the quantum degrees of freedom of black holes in string theory.
We make some observations regarding string/black hole correspondence with a view to understanding the nature of the quantum degrees of freedom of a black hole in string theory. In particular, we compare entropy change in analogous string and black hole processes in order to support the interpretation of the area law entropy as arising from stringy constituents.
We review some applications of Type 0 string theory in the context of the AdS/CFT correspondence.
We present an example of the string correspondence: a relation between two classical string solutions - one in Minkowski spacetime and another one in the AdS spacetime. The first solution describes a $2$d motion of the string with massive ends and was derived in (https://doi.org/10.1103/PhysRevD.13.2364). The second solution is the accelerating string solution in the $\textrm{AdS}_3$ spacetime and describes a heavy quark-antiquark pair (arXiv:0804.1343).
We study the holographic principle of the two-point function in the case of a spinning string in the AdS/CFT correspondence. Following the general method proposed by Yoneya et al. for the bulk-boundary correspondence in the large $J$ limit, we study the spinning string solution which starts and ends at the boundary. We then show that the spinning string solution directly gives a two-point function that is consistent with the spin chain picture in gauge theory.
We consider a thought experiment in which an energetic massless string probes a "stringhole" (a heavy string lying on the correspondence curve between strings and black holes) at large enough impact parameter for the regime to be under theoretical control. The corresponding, explicitly unitary, $S$-matrix turns out to be perturbatively sensitive to the microstate of the stringhole: in particular, at leading order in $l_s/b$, it depends on a projection of the stringhole's Lorentz-contracted quadrupole moment. The string-black hole correspondence is therefore violated if one assumes quantum hair…
This thesis investigates correspondences between open and closed strings. This is done on the level of coupled open-closed moduli spaces and from a string field theoretic point of view. The construction of boundary string field theory on Wess-Zumino-Witten models leads to a conjecture on closed string backgrounds appearing as non-local operators in open string field theory. Sample computations for tachyon condensation leading to curved branes support this conjecture. Additional steps are taken to study supersymmetric string theories on Calabi-Yau manifolds in the presence of bulk and boundary …
We show that weak-coupled two-dimensional dilaton gravity on Anti-de Sitter space can be described by the dynamics of an open string. Neumann and Dirichlet boundary conditions for the string lead to two different realizations of the Anti-de Sitter/Conformal Field Theory correspondence. In particular, in the Dirichlet case the thermodynamical entropy of two-dimensional black holes can be exactly reproduced by counting the string states.
We calculate emission rates of a massless state from a highly excited rotating string in perturbative bosonic open string theory. By averaging huge degeneracies of initial string states with specifying the mass and a single component of the angular momentum, we find thermal spectrum in a wide range of the angular momentum. We derive the temperature that characterizes the thermal spectrum from the partition function of a single rotating string from which we also find the entropy and the angular velocity of rotating strings. We also argue based on these quantities the Horowitz-Polchinski corresp…
We discuss Gubser-Klebanov-Polyakov proposal for the gauge/string theory correspondence for gauge theories in curved space. Specifically, we consider Klebanov-Tseytlin cascading gauge theory compactified on S^3. We explain regime when this gauge theory is a small deformation of the superconformal N=1 gauge theory on the world volume of regular D3-branes at the tip of the conifold. We study closed string states on the leading Regge trajectory in this background, and attempt to identify the dual gauge theory twist two operators.
We study closed string tachyon condensation on general non-supersymmetric orbifolds of C^2. Extending previous analyses on Abelian cases, we present the classification of quotients by discrete finite subgroups of GL(2; C) as well as the generalised Hirzebruch-Jung continued fractions associated with the resolution data. Furthermore, we discuss the intimate connexions with certain generalised versions of the McKay Correspondence.
We discuss the entropy for the extremal BTZ black hole and the extremal EBTZ black hole. The EBTZ black hole means the BTZ black hole embedded in a five-dimensional(5D) black hole. The six-dimensional(6D) black string with traveling waves is introduced as a concrete model for realizing the AdS/CFT correspondence. The traveling waves carry the momentum distribution $p(u)$ which plays an important role in counting the entropy and establishing the correspondence. It turns out that the EBTZ black hole is consistent with the AdS/CFT correspondence.
We reproduce the correspondence between open string states |n> and BMN operators O_n in N=2 supersymmetric gauge theory using a worldsheet computation with the relation <B|n>=O_n, where <B| is a boundary state of D3-branes. We regard the NS ground states and their excitations with respect to a bosonic oscillator as the states |n> and obtain a chiral operator and BMN operators, respectively, in correspondence to them. Because we take the coupling constant to be weak and the background spacetime to be flat Minkowski, not AdS, the string states |n> are circular waves around the D3-branes, instead…
This paper analyzes the effect of curved closed string backgrounds on the stability of D-branes within boundary string field theory. We identify the non-local open string background that implements shifts in the closed string background and analyze the tachyonic sector off-shell. The renormalization group flow reveals some characteristic properties, which are expected for a curved background, like the absence of a stable space-filling brane. In 3-dimensions we describe tachyon condensation processes to lower-dimensional branes, including a curved 2-dimensional brane. We argue that this 2-brane…
In the context of the Penrose/BMN limit of the AdS/CFT correspondence, we consider four-impurity BMN operators in Yang-Mills theory, and demonstrate explicitly their correspondence to four-oscillator states in string theory. Using the dilatation operator on the gauge-theory side of the correspondence, we calculate matrix elements between four-impurity states. Since conformal dimensions of gauge-theory operators correspond to light-cone energies of string states, these matrix elements may be compared with the string-theory light-cone Hamiltonian matrix elements calculated in the plane-wave back…
We present evidence for the factorization of the world-sheet path integrals for 2d conformal field theories on the disk into bulk and boundary contributions. This factorization is then used to reinterpret a shift in closed string backgrounds in terms of boundary deformations in background independent open string field theory. We give a proof of the factorization conjecture in the cases where the background is represented by WZW and related models.
Size and Shape of Rotating Strings and the Correspondence to Black Holes
本研究基于黑洞与自旋基本弦的对应关系，计算不同角动量下旋转弦的尺寸并与黑洞比较，发现小角动量下尺寸比的自旋依赖性一致，大角动量下行为不同，还提出可准确描述各角动量下旋转弦尺寸的随机游走模型。
In this paper, we demonstrate that locally, the $α^{\prime}$ expansion of a string propagating in AdS can be summed into a closed expression, where the $α'$ dependence is manifested. The T-dual of this sum exactly matches the expression controlling all genus expansion in the Goparkumar-Vafa formula, which in turn also matches the loop expansion of the Chern-Simons gauge theory. We therefore find an exact correspondence between the $α^{\prime}$ expansion for a string moving in AdS and the genus expansion of a string propagating in four dimensional flat spacetime. We are then able to give a clos…
Using target space null reduction of the Polyakov action we find a novel covariant action for strings moving in a torsional Newton-Cartan geometry. Sending the string tension to zero while rescaling the Newton-Cartan clock 1-form, so as to keep the string action finite, we obtain a non-relativistic string moving in a new type of non-Lorentzian geometry that we call $U(1)$-Galilean geometry. We apply this to strings on $AdS_5 \times S^5$ for which we show that the zero tension limit is realized by the Spin Matrix theory limits of the AdS/CFT correspondence. This is closely related to limits of …
In this article we review the conditions for the validity of the gauge/gravity correspondence in both supersymmetric and non-supersymmetric string models. We start by reminding what happens in type IIB theory on the orbifolds C^2/Z_2 and C^3/(Z_2 x Z_2), where this correspondence beautifully works. In these cases, by performing a complete stringy calculation of the interaction among D3 branes, it has been shown that the fact that this correspondence works is a consequence of the open/closed duality and of the absence of threshold corrections. Then we review the construction of type 0 theories …
We present a detailed discussion of the duality between dilaton gravity on AdS_2 and open strings. The correspondence between the two theories is established using their symmetries and field theoretical, thermodynamic, and statistical arguments. We use the dual conformal field theory to describe two-dimensional black holes. In particular, all the semiclassical features of the black holes, including the entropy, have a natural interpretation in terms of the dual microscopic conformal dynamics. The previous results are discussed in the general framework of the Anti-de Sitter/Conformal Field Theo…
Employing the string bit formalism of hep-th/0209215, we identify the basis transformation that relates BMN operators in N=4 gauge theory to string states in the dual string field theory at finite g_2=J^2/N. In this basis, the supercharge truncates at linear order in g_2, and the mixing amplitude between 1 and 2-string states precisely matches with the (corrected) answer of hep-th/0206073 for the 3-string amplitude in light-cone string field theory. Supersymmetry then predicts the order g_2^2 contact term in the string bit Hamiltonian. The resulting leading order mass renormalization of string…
We review, in a self-contained and pedagogical manner, recent developments and techniques for the evaluation of the scattering amplitudes of planar N=4 SYM theory at both weak and strong coupling. Special emphasis is placed on the newly discovered connection between a special class of amplitudes and the expectation values of particular cusped light-like Wilson loops.
String theory with perimeter action is tensionless by its geometrical nature and has pure massless spectrum of higher spin gauge particles. I demonstrate that liner transformation of the world-sheet fields defines a map to the SO(D,D) sigma model equipped by additional Abelian constraint, which breaks SO(D,D) to a diagonal SO(1,D-1). The effective tension is equal to the square of the dimensional coupling constant of the perimeter action. This correspondence allows to view the perimeter action as a "square root" of the Nambu-Goto area action. The aforementioned map between tensionless strings …
We review some recent results on the extension of the gauge/gravity correspondence to include matter in the fundamental representation by adding D-branes to the supergravity backgrounds. Working in the quenched approximation, in which the D-branes are considered as probes, we show how to compute the meson spectrum for a general case of brane intersections which are dual to supersymmetric gauge theories with matter supermultiplets in several dimensions.
The AdS/CFT correspondence is an exact duality between string theory in anti-de Sitter space and conformal field theories on its boundary. Inspired in this correspondence some relations between strings and non conformal field theories have been found. Exact dualities in the non conformal case are intricate but approximations can reproduce important physical results. A simple approximation consists in taking just a slice of the AdS space with a size related to an energy scale. Here we will discuss how this approach can be used to reproduce the scaling of high energy QCD scattering amplitudes. A…
We use the anti-de Sitter (AdS) conformal field theory correspondence to calculate the conserved charges and the Euclidean actions of the charged rotating black string in four dimensions both in the canonical and the grand-canonical ensemble. The four-dimensional solution of the Einstein-Maxwell equations with a positive cosmological constant is introduced, and its conserved quantities and actions for fixed charge and fixed electric potential are calculated. We also study the thermodynamics of the asymptotically AdS black strings and perform a stability analysis both in the canonical and the g…
We study the localization of gravity on string-like defects in codimension two. We point out that the gravity-localizing `local cosmic string' spacetime has an orbifold singularity at the horizon. The supergravity embedding and the AdS/CFT correspondence suggest ways to resolve the singularity. We find two resolutions of the singularity that have a semiclassical gravity description and study their effect on the low-energy physics on the defect. The first resolution leads, at long distances, to a codimension one Randall-Sundrum scenario. In the second case, the infrared physics is like that of …
We propose a scenario of gauge-string correspondence by relating the SU(3) colour group to hidden space-time isometries originating from extra dimensions. These isometries ($α$-symmetries) are the special symmetries of RNS superstring theories under global non-linear space-time transformations. The vertex operators for the octet of gluons are constructed by the procedure of ``photon painting'', that is, with the SU(3) subgroup of the $α$-symmetry generators acting on a regular open string photon, so the corresponding open string excitations are in the adjoint of SU(3). Remarkably, the operator…
Non-degenerate perturbation theory, which was used to calculate the scale dimension of operators on the gauge theory side of the correspondence, breaks down when effects of triple trace operators are included. We interpret this as an instability of excited single-string states in the dual string theory for decay into the continuum of degenerate 3-string states. We apply time-dependent perturbation theory to calculate the decay widths from gauge theory. These widths are new gauge theory data which can be compared with future calculations in light cone string field theory.
This report presents some studies of the gauge/string theory correspondence, a deep relation that is possible to establish between quantum field theories with local gauge symmetry and superstring theories including gravity. In its original version, known as AdS/CFT duality, the correspondence involves N=4 Super Yang-Mills theory in four space-time dimensions, which is a superconformal theory with a high degree of supersymmetry, thus very far from describing the physical world. We explore extensions of the correspondence towards less supersymmetric and non-conformal gauge theories. Specifically…
We find a Polyakov-type action for strings moving in a torsional Newton-Cartan geometry. This is obtained by starting with the relativistic Polyakov action and fixing the momentum of the string along a non-compact null isometry. For a flat target space, we show that the world-sheet theory becomes the Gomis-Ooguri action. From a target space perspective these strings are non-relativistic but their world-sheet theories are still relativistic. We show that one can take a scaling limit in which also the world-sheet theory becomes non-relativistic with an infinite-dimensional symmetry algebra given…
A world-sheet sigma model approach is applied to string theories dual to four-dimensional gauge theories, and semi-classical soliton solutions representing highly excited string states are identified which correspond to gauge theory operators with relatively small anomalous dimensions. The simplest class of such states are strings on the leading Regge trajectory, with large spin in AdS_5. These correspond to operators with many covariant derivatives, whose anomalous dimension grows logarithmically with the space-time spin. In the gauge theory, the logarithmic scaling violations are similar to …
We use the correspondence between string states and local operators on the world-sheet boundary defined by vertex operators in open string theory to put in correspondence, holographically, the bosonic open string with the large N limit of a mechanical system living on the world-sheet boundary. We give a natural interpretation of this system in terms of a one-dimensional stochastic process and show that the correspondence takes the form of a map between two conformal field theories with central charge c=24 and c=1.
We will study the AdS/CFT correspondence in an intermediate region between the strong form of this correspondence (string theory on AdS being dual to a boundary CFT), and the weak form of this correspondence (supergravity on AdS being dual to a boundary CFT). We will go beyond the supergravity approximation in the AdS by using the fact that strings have an extended structure. We will also calculate the CFT dual to such string corrections in the bulk, and demonstrate that they are consistent with the strong form of the AdS/CFT correspondence. So, even though the conformal dimensions of both the…
In these lectures we describe the attempt to extract the expectation values of Wilson loops from the string/gauge correspondence. We start with the original calculation in $AdS_5$. It is then extended to the non-conformal background of $D_p$ in the near horizon limit. We discuss the computation at finite temperature. Supergravity models that admit confinement in 3d and 4d are described. A theorem that determines the classical values of loops associated with a generalized background is derived.In particular we determine sufficient conditions for confining behavior. We then apply the theorem to …
The PP-wave/SYM proposal in its original form emphasizes a duality relation between the masses of the string states and the anomalous dimensions of the corresponding BMN operators in gauge theory, the mass--dimension type duality. In this paper, we give evidence in favour of another duality relation of the vertex--correlator type, which relates the coefficients of 3-point correlators of BMN operators in gauge theory to 3-string vertices in lightcone string field theory in the pp-wave background. We verify that all the available field theory results in the literature, as well as the newly obtai…
We construct semi-classical string solutions of the Schrödinger $Sch_5 \times S^5$ spacetime, which is conjectured to be the gravity dual of a non-local dipole-deformed CFT. They are the counterparts of the giant magnon and spiky string solutions of the undeformed $AdS_5 \times S^5$ to which they flow when the deformation parameter is turned off. They live in an $S^3$ subspace of the five-sphere along the directions of which the $B$-field has non-zero components having also extent in the $Sch_5$ part of the metric. Finally, we speculate on the form of the dual field theory operators.
It is known that YM_2 with gauge group SU(N) is equivalent to a string theory with coupling g_s=1/N, order by order in the 1/N expansion. We show how this results can be obtained from the bosonization of the fermionic formulation of YM_2, improving on results in the literature, and we examine a number of non-perturbative aspects of this string/YM correspondence. We find contributions to the YM_2 partition function of order exp{-kA/(πα' g_s)} with k an integer and A the area of the target space, which would correspond, in the string interpretation, to D1-branes. Effects which could be interpret…
A study of string theory and the AdS/CFT correspondence
本文综述了弦理论及AdS/CFT对应的原始推导，涵盖大N展开、玻色弦、D膜、II型超弦及超对称膜，并讨论全息词典等性质。
We study the stability of some classical string worldsheet solutions employed for computing the potential energy between two static fundamental quarks in confining and non-confining gravity duals. We discuss the fixing of the diffeomorphism invariance of the string action, its relation with the fluctuation orientation and the interpretation of the quark mass substraction worldsheet needed for computing the potential energy in smooth (confining) gravity background. We consider various dual gravity backgrounds and show by a numerical analysis the existence of instabilities under linear fluctuati…
I was asked to give a brief review of the black hole-string correspondence as a warm-up for a longer SITP-group discussion of a recent paper by Chen, Maldacena, and Witten. Here are my notes in written form.
We compute the annulus diagram corresponding to the interaction of a fractional D3 brane with a gauge field on its world-volume and a stack of N fractional D3 branes on the orbifolds C^2 /Z_2 and C^3/Z_2 x Z_2. We show that its logarithmic divergence can be equivalently understood as due either to massless open string states circulating in the loop or to massless closed string states exchanged between two boundary states. This follows from the fact that, under open/closed string duality, massless states in the open and closed string channels are matched into each other without mixing with mass…
We establish a translation dictionary between open and closed strings, starting from open string field theory. Under this correspondence, (off-shell) level-matched closed string states are represented by star algebra projectors in open string field theory. Particular attention is paid to the zero mode sector, which is indispensable in order to generate closed string states with momentum. As an outcome of our identification, we show that boundary states, which in closed string theory represent D-branes, correspond to the identity string field in the open string side. It is to be remarked that c…
Based on the holographic conjecture for superstrings on Dp-brane backgrounds and the dual (p+1)-dimensional gauge theory ($0\le p\le 4$) given in hep-th/0308024 and hep-th/0405203, we continue the study of superstring amplitudes including string higher modes ($n\ne 0$). We give a prediction to the two-point functions of operators with large R-charge J. The effect of stringy modes do not appear as the form of anomalous dimensions except for p=3. Instead, it gives non-trivial correction to the two-point functions for supergravity modes. For p=4, the scalar two-point functions for any n behave li…
When we vary the moduli of a compactification it may become entropically favourable at some point for a state of branes and strings to rearrange itself into a new configuration. We observe that for the elementary string with two large charges such a rearrangement happens at the `correspondence point' where the string becomes a black hole. For smaller couplings it is entropically favourable for the excitations to be vibrations of the string, while for larger couplings the favoured excitations are pairs of solitonic 5-branes attached to the string; this helps resolve some recently noted difficul…
We briefly review the recent progress concerning the application of the hidden integrability to the derivation of the stringy/brane picture for the high energy QCD.
I present the sketch of a "physicist's" derivation of the AdS/CFT correspondence for the original pair, string theory in $AdS_5\times S^5$ vs. ${\cal N}=4$ SYM, based on the pp wave limit, and deviations from it. I show that one can reverse the logic, and derive the action of ${\cal N}=4$ SYM, as kinetic terms plus vertices, as well as the elements of its path integral, from string theory on the pp wave. One can also treat consistently deviations from the "strings on the pp wave" limit, starting from the SYM side, and a priori reconstruct the full $AdS_5\times S^5$ geometry perturbatively, as …
The pp-wave/SYM correspondence is an equivalence relation, H_{string}= Delta -J, between the Hamiltonian H_{string} of string field theory in the pp-wave background and the dilatation operator Delta in N=4 Super Yang-Mills in the double scaling limit. We calculate matrix elements of these operators in string field theory and in gauge theory.In the string theory Hilbert space we use the natural string basis,and in the gauge theory we use the basis which is isomorphic to it. States in this basis are specific linear combinations of the original BMN operators, and were constructed previously for t…
We investigate the quasinormal spectrum of electromagnetic perturbations of rotating black strings. Among the solutions of Einstein equations in the presence of a negative cosmological constant there are asymptotically anti-de Sitter (AdS) black holes whose horizons have the topology of a cylinder. The stationary version of these AdS black holes represents rotating black strings. The conformal field theory (CFT) dual of a black string lives in a Minkowski space with a compact dimension. On the basis of the AdS/CFT duality, we interpret a CFT plasma moving with respect to the preferred rest fra…
The string-black hole correspondence is considered in the context of the correspondence principle proposed recently by Horowitz and Polchinski. We demonstrate that the entropy of string states and the entropy of a Schwarzschild black hole can be matched including the subleading terms which depend on mass logarithmically. We argue the necessity to include the string interaction (with coupling $g$) in the consideration and propose the $g^2$-dependent modification of the string entropy. The matching of it with the entropy of Schwarzschild black hole is analyzed.
We study non-Abelian vortex strings in four-dimensional (4D) $\mathcal{N} = 2$ supersymmetric QCD with U$(N=2)$ gauge group and $N_f=4$ flavors of quark hypermultiplets. It has been recently shown that these vortices behave as critical superstrings. The spectrum of closed string states in the associated string theory was found and interpreted as a spectrum of hadrons in 4D $\mathcal{N} = 2$ supersymmetric QCD. In particular, the lowest string state appears to be a massless BPS "baryon." Here we show the occurrence of this stringy baryon using a purely field-theoretic method. To this end we stu…
We review the caloron correspondence between $G$-bundles on $M \times S^1$ and $ΩG$-bundles on $M$, where $ΩG$ is the space of smooth loops in the compact Lie group $G$. We use the caloron correspondence to define characteristic classes for $ΩG$-bundles, called string classes, by transgression of characteristic classes of $G$-bundles. These generalise the string class of Killingback to higher dimensional cohomology.
In a string calculation to order $α'^3$, we compute an eight-derivative four-dilaton term in the type IIB effective action. Following the AdS prescription, we compute the order $(g_{YM}^2N_c)^{-3/2}$ correction to the four-point correlation function involving the operator $tr F^2$ in four dimensional N=4 super Yang-Mills using the string corrected type IIB action extending the work of Freedman et al. (hep-th/9808006). In the limit where two of the Yang-Mills operators approach each other, we find that our correction to the four-point correlation functions develops a logarithmic singularity. We…
We investigate a Π-shape Wilson loop in N=4 super Yang--Mills theory, which lies partially at the light-cone, and consider an associated open superstring in AdS_5 x S^5. We discuss how this Wilson loop determines the anomalous dimensions of conformal operators with large Lorentz spin and present an explicit calculation in perturbation theory to order λ. We find the minimal surface in the supergravity approximation, that reproduces the Gubser, Klebanov and Polyakov prediction for the anomalous dimensions at large λ=g_YM^2 N, and discuss its quantum-mechanical interpretation.
Closed string diagrams are derived from cubic open string field theory using a gauge fixed kinetic operator. The basic idea is to use a string propagator that does not generate a boundary to the world sheet. Using this propagator and the closed string vertex, the moduli space of closed string surfaces is covered, so closed string scattering amplitudes should be reproduced. This kinetic operator could be a gauge fixed form of the string field theory action around the closed string vacuum.
The AdS/CFT correspondence predicts a phase transition in Wilson loop correlators in the strong coupling N=4, D=4 SYM theory which arises due to instability of the classical string stretched between the loops. We study this transition in detail by solving equations of motion for the string in the particular case of two circular Wilson loops. The transition is argued to be smoothened at finite `t Hooft coupling by fluctuations of the string world sheet and to be promoted to a sharp crossover. Some general comments about Wilson loop correlators in gauge theories are made.
We calculate the complete closed string high energy scattering amplitudes (HSA) in the Regge regime for arbitrary mass levels. As an application, we deduce the complete ratios among closed string HSA in the fixed angle regime by using Stirling number identities. These results are in contrast with the incomplete set of closed string HSA in the fixed angle regime calculated previously. The complete forms of the fixed angle amplitudes, and hence the ratios, were not calculable previously without the input of zero-norm state calculation. This is mainly due to the lack of saddle point in the fixed …
We investigate a classical open-closed string field theory whose open string sector is given by boundary string field theory. The open-closed interaction is introduced by the overlap of a boundary state with a closed string field. With the help of the Batalin-Vilkovisky formalism, the closed string sector is determined to be the HIKKO closed string field theory. We also discuss the gauge invariance of this theory in both open and closed string sides.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。