D. S. Kulshreshtha
Conformally gauge-fixed Polyakov D1 brane action is seen to be a constrained sys tem in the sense of Dirac when it is considered on the light-front in contrast t o the case when it is consdired in the instant-form. The model is quantized usin g the standard constraint quantization techniques on the light-front.
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Light-front quantization of the conformally gauge-fixed Polyakov D1 brane action with a scalar dilaton field is studied using the equal light-cone world-sheet time framework.
In this paper, we study the M-brane description of the Wilson-Polyakov surfaces in six-dimensional (2, 0) field theory at finite temperature. We investigate the membrane solution dual to a straight Wilons-Polyakov surface and compute the interaction potential between two parallel straight strings by using AdS/CFT correspondence. Furthermore we discuss the M5-brane solutions dual to various Wilson-Polyakov surfaces. Finally we obtain an universal result about M5-brane solutions in generic backgrounds.
We study two Polyakov loop correlators in large $N$ limit of ${\cal{N}}=4$ super Yang-Mills theory at finite temperature using the AdS-Schwarzschild black hole. In the case that one of the two loops is of the anti-symmetric representation, we use D5-branes to evaluate them. The phase structure of these correlators is also examined. A previous result, derived in hep-th/9803135 and hep-th/9803137, is realized as a limiting case.}
Closed string field theory is constructed by stochastically quantizing a matrix model for Polyakov loops that describes phases of a large N gauge theory at finite temperature. Coherent states in this string field theory describes winding string condensation which has been expected to cause a topology change from thermal AdS geometry to AdS-Schwarzschild black hole geometry. D-branes in this closed string field theory is also discussed. Slightly extended version of a talk given at CosPA 2007, Nov.13-15, Taipei, Taiwan.
We study holographic probes dual to heavy quark impurities interpolating between fundamental and symmetric/antisymmetric tensor representations in strongly coupled N=4 supersymmetric gauge theory. These correspond to non-conformal D3- and D5-brane probe embeddings in AdS_5 x S^5 exhibiting flows on their world-volumes. By examining the asymptotic regimes of the embeddings and the one-point function of static fields sourced by the boundary impurity, we conclude that the D5-brane embedding describes the screening of fundamental quarks in the UV into an antisymmetric source in the IR, whilst the …
We study the expectation value of a Polyakov-Maldacena loop that wraps the thermal circle k times in strongly coupled N=4 super Yang-Mills theory. This is achieved by considering probe D3 and D5 brane embeddings in the dual black hole geometry. In contrast to multiply wound spatial Wilson loops, nontrivial dependence on k is captured through D5 branes. We find N^{-2/3} corrections, reminiscent of the scaling behaviour near a Gross-Witten transition.
Aspects of d=4, N=4 superconformal U(N) gauge theory are studied at finite temperature. Utilizing dual description of large $N$ and strong coupling limit via Type IIB string theory compactification on Schwarzschild anti-de Sitter spacetime, we study correlations of Wilson-Polyakov loops and heavy quark potential thereof. We find that the heavy quark potential is Coulomb-like and has a finite range, as expected for gauge theory in high temperature, deconfinement phase. The potential exhibits finite temperature scaling consistent with underlying conformal invariance. We also study isolated heavy…
In this paper we re-derive the effective Nambu-Goto theory result for the Polyakov loop correlator, starting from the free bosonic string and using a covariant quantization. The boundary conditions are those of an open string attached to two D0-branes at spatial distance R, in a target space with compact euclidean time. The one-loop free energy contains topologically distinct sectors corresponding to multiple covers of the cylinder in target space bordered by the Polyakov loops. The sector that winds once reproduces exactly the Nambu-Goto partition function. In our approach, the world-sheet du…
In string theory, the consequences of replacing the measure of integration $\sqrt{-γ}d^2 x$ in the Polyakov's action by $Φd^2 x$ where $Φ$ is a density built out of degrees of freedom independent of the metric $γ_{ab}$ defined in the string are studied. The string tension appears as an integration constant of the equations of motion. The string tension can change in different parts of the string due to the coupling of gauge fields and point particles living in the string. The generalization to higher dimensional extended objects is also studied. In this case there is no need of a fine tuned co…
We study the procedure that allows to rewrite the actions of some modified gravity theories like mimetic gravity and Regge-Teitelboim embedding theory as Einstein-Hilbert actions with additional matter contributions. It turns out that this procedure can be applied to brane action, which lead to a polynomial brane action. We also examine the connection between this procedure and Polyakov trick in string theory.
The Polyakov loop of an operator in the anti-symmetric representation in N=4 SYM theory on spacial R^3 is calculated, to leading order in 1/N and at large 't Hooft coupling, by solving the saddle point equations of the corresponding quantum impurity model. Agreement is found with previous results from the supergravity dual, which is given by a D5-brane in an asymptotically AdS_5 x S^5 black brane background. It is shown that the azimuth angle, at which the dual D5-brane wraps the S^5, is related to the spectral asymmetry angle in the spectral density associated with the Green's function of the…
We introduce a new action $S_{standard}^{(ρ,h; Φ,g,B,C)}$ for D-branes that is to D-branes as the Polyakov action is to fundamental strings. This `standard action' is abstractly a non-Abelian gauged sigma model --- based on maps $φ: (X^{\!A\!z},E;\nabla)\rightarrow Y$ from an Azumaya/matrix manifold $X^{\!A\!z}$ with a fundamental module $E$ with a connection $\nabla$ to $Y$ --- enhanced by the dilaton term, the gauge-theory term, and the Chern-Simons/Wess-Zumino term that couples $(φ,\nabla)$ to Ramond-Ramond field. In a special situation, this new theory merges the theory of harmonic maps an…
We derive the noncommutative Dirac-Born-Infeld action for the $D$-brane, which governs dynamics of $D$-brane with a NS-NS $B$-field in the low energy regime. Depending on some details of the path integral prescriptions, both ordinary Dirac-Born-Infeld action and noncommutative one can be obtained by evaluating the same Polyakov string path integral for the open string ending on the $D$-brane. Thus, it establishes the equivalence of the noncommutative Dirac-Born-Infeld action and the ordinary one.
The dynamics (in light-cone time) of the tachyon on an unstable brane in the background of a dilaton linear along a null coordinate is a non-local reaction-diffusion type equation, which admits a travelling front solution. We analyze the (in-)stability of this solution using linearized perturbation theory. We find that the front solution obtained in singular perturbation method is stable. However, these inhomogenous solutions (unlike the homogenous solution) also have Lyapunov exponents corresponding to unstable modes around the (meta-)stable vacuum.
We consider probe p-branes dynamics in string theory backgrounds of general type. We use an action, which interpolates between Nambu-Goto and Polyakov type actions. This allows us to give a unified description for the tensile and tensionless branes. Firstly, we perform our analysis in the frequently used static gauge. Then, we obtain exact brane solutions in more general gauges. The same approach is used to study the Dirichlet p-brane dynamics and here exact solutions are also found. As an illustration, we apply our results to the brane world scenario in the framework of the mirage cosmology a…
A master action for the bosonic p-brane, interpolating between the Nambu--Goto and Polyakov formalisms, is discussed. The fundamental arbitrariness of extended structures (p-brane) embeded in space time manifold has been exploited to build an independent metric in the brane world volume. The cosmological term for the generic case follows naturally in the scheme. The dynamics of the structure leads to a natural emergence of the A--D--M like split of this world volume. The role of the gauge symmetries vis-à-vis reparametrization symmetries is analyzed by a constrained Hamiltonian approach.
We present a generalization of the string's Polyakov action that describes a conformally invariant four dimensional brane. The new extended object is very different from the traditional D-branes of string theory, but, nevertheless, shares some structural similarities with the string, especially when it comes to the low-energy limit of small tension. We introduce a rather rich structure of tensors that can play a role at low energies. In analogy with the bosonic string, we initiate the quantization of the new brane discussing the extent in which it produces a critical dimension of spacetime and…
The t'Hooft-Polyakov monopole mass can be substantially altered, in the thick GS and HC brane-world setup, and can be employed to constrain the brane thickness limit. In this work, we comprise a brief review regarding gauge fields localization in the string-like six dimensional brane-world models setup. The correction to the Coulomb's law in two models is studied. Besides, the monopole features are investigated from the point of view of the gauge fields localization in the string-like brane-worlds and its thickness.
Concise summary of the recent progress in the search for the world-volume action for multiple M2 branes. After a recent discovery of simplified version of BLG action, which is based on the ordinary Lie-algebra structure, does not have coupling constants and extra dynamical fields, attention should be switched to the study of M2 brane dynamics. A viable brane analogue of Polyakov formalism and Belavin-Knizhnik theorem for strings can probably be provided by Palatini formalism for 3d (super)gravity.
We consider the inhomogeneous decay of an unstable D-brane of bosonic string theory in a linear dilaton background in a light-cone frame. At the lowest level, the dynamical equation that describes this process is a generalisation (that includes nonlocality and time delay) of a reaction-diffusion equation studied by Fisher (and others). We argue that the equation of motion of the cubic open string field theory is satisfied at least to the second order when we start with this `Fisher deformation', a marginal operator which has a simple pole term in its OPE. We also compute the one-point function…
We present regular solutions for a brane world scenario in the form of a 't Hooft-Polyakov monopole living in the three-dimensional spherical symmetric transverse space of a seven-dimensional spacetime. In contrast to the cases of a domain-wall in five dimensions and a string in six dimensions, there exist gravity-localizing solutions for both signs of the bulk cosmological constant. A detailed discussion of the parameter space that leads to localization of gravity is given. A point-like monopole limit is discussed.
We study Witten's cubic open string field theory on multiple $Dp$-branes. On multiple $Dp$-branes the string fields carry $U(N)$ group indices. Mapping the string world-sheet onto the upper half complex plane and evaluating the Polyakov string path integral of Witten's cubic open string, we obtain a Fock space representation of one, two and three-string vertex operators. In the low energy region, the system is described by massless gauge fields and massless scalar fields, carrying $U(N)$ group indices. The two-string vertex induces mass terms for the gauge fields and the scalar fields. The cub…
Carroll Limit of $\mathcal{O}(F^2)$ $\text{D}_p$-branes from Kaluza--Klein-like Null reduction in the Polyakov Formulation
本文通过Polyakov-KK途径构造$\text{O}(F^2)$截断$\text{D}_p$-膜的电、磁Carroll极限，揭示其与无$\text{U}(1)$ ILST弦的差异，分析自由度及与无张力/零弦的关联。
We discuss non-perturbative effects in the ABJM model due to monopole instantons. We begin by constructing the instanton solutions in the $U(2)\times U(2)$ model, explicitly, and computing the Euclidean action. The Wick-rotated Lagrangian is complex and its BPS monopole instantons are found to be a delicate version of the usual 't Hooft-Polyakov monopole solutions. They are generically 1/3 BPS but become 1/2 BPS at special locus in the moduli space of two M2-branes, yet each instanton carries eight fermionic zero modes, regardless of the vacuum choice. The low energy effective action induced b…
We argue that different aspects of Light-Front QCD at confined phase can be recovered by the Matrix Quantum Mechanics of D0-branes. The concerning Matrix Quantum Mechanics is obtained from dimensional reduction of pure Yang-Mills theory to 0+1 dimension. The aspects of QCD dynamics which are studied in correspondence with D0-branes are: 1) phenomenological inter-quark potentials, 2) whiteness of hadrons and 3) scattering amplitudes. In addition, some other issues such as the large-N behavior, the gravity--gauge theory relation and also a possible justification for involving ``non-commutative c…
We consider the type 0 theories, obtained from the closed NSR string by a diagonal GSO projection which excludes space-time fermions, and study the D-branes into these theories. The low-energy dynamics of N coincident D-branes is governed by a U(N) gauge theory coupled to adjoint scalar fields. It is tempting to look for the type 0 string duals of such bosonic gauge theories in the background of the R-R charged p-brane classical solutions. This results in a picture analogous to the one recently proposed by Polyakov (hep-th/9809057). One of the serious problems that needs to be resolved is the …
We propose a novel prescription to take off the square root of Nambu-Goto action for a p-brane, which generalizes the Brink-Di Vecchia-Howe-Tucker or also known as Polyakov method. With an arbitrary decomposition as d+n=p+1, our resulting action is a modified d-dimensional Polyakov action which is gauged and possesses a Nambu n-bracket squared potential. We first spell out how the (p+1)-dimensional diffeomorphism is realized in the lower dimensional action. Then we discuss a possible gauge fixing of it to a direct product of $d$-dimensional diffeomorphism and n-dimensional volume preserving di…
We construct a covariant open bosonic string field theory on multiple D-branes, which reduces to a non-Abelian group Yang-Mills gauge theory in the zero-slope limit. Making use of the first quantized open bosonic string in the proper time gauge, we convert the string amplitudes given by the Polyakov path integrals on string world sheets into those of the second quantized theory. The world sheet diagrams generated by the constructed open string field theory are planar in contrast to those of the Witten's cubic string field theory. However, the constructed string field theory is yet equivalent t…
These notes give a pedagogical introduction to D-branes and Matrix theory. The development of the material is based on super Yang-Mills theory, which is the low-energy field theory describing multiple D-branes. The main goal of these notes is to describe physical properties of D-branes in the language of Yang-Mills theory, without recourse to string theory methods. This approach is motivated by the philosophy of Matrix theory, which asserts that all the physics of light-front M-theory can be described by an appropriate super Yang-Mills theory.
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 construct dyon solutions on a collection of coincident D4-branes, obtained by applying the group of T-duality transformations to a type I SO(32) superstring theory in 10 dimensions. The dyon solutions, which are exact, are obtained from an action consisting of the non-abelian Dirac-Born-Infeld action and Wess-Zumino-like action. When one of the spatial dimensions of the D4-branes is taken to be vanishingly small, the dyons are analogous to the 't Hooft/Polyakov monopole residing in a 3+1 dimensional spacetime, where the component of the Yang-Mills potential transforming as a Lorentz scalar …
In these lectures we start with a pedagogical introduction of the properties of open and closed superstrings and then, using the open/closed string duality, we construct the boundary state that provides the description of the maximally supersymmetric Dp branes in terms of the perturbative string formalism. We then use it for deriving the corresponding supergravity solution and the Born-Infeld action and for studying the properties of the maximally supersymmetric gauge theories living on their worldvolume. In the last section of these lectures we extend these results to less supersymmetric and …
The Newtonian character of gauge theories on a light front requires that the longitudinal momentum P^+, which plays the role of Newtonian mass, be conserved. This requirement conflicts with the standard definition of the force between two sources in terms of the minimal energy of quantum gauge fields in the presence of a quark and anti-quark pinned to points separated by a distance R. We propose that, on a light front, the force be defined by minimizing the energy of gauge fields in the presence of a quark and an anti-quark pinned to lines (1-branes) oriented in the longitudinal direction sing…
M(atrix) theory defines light-front description of M-theory boosted along positive direction of eleventh, M-coordinate. Rank of M(atrix) gauge group is directly related to M-momentum $P_{11} = N / R_{11}$ or, equivalently, to total number of D0-partons. Alternatively, M-theory may be boosted along opposite direction of M-coordinate, for which the theory consists only of anti-D0 partons. In M(atrix) theory description, we interpret this as analytic continuation of dimension of the gauge group: $U(-N) \sim U(N)$, $SO(-2N) \sim USp(2N)$ and $USp(-2N) \sim SO(2N)$. We check these reciprocity relat…
Rederiving the one-loop divergences for the most general coupling of the open string sigma model by the heat kernel technique, we distinguish the classical background field from the mean field of the effective action. The latter is arbitrary, i.e. does not fulfil the boundary conditions. As a consequence a new divergent counter term strongly suggests the introduction of another external one-form field (beside the usual gauge field), coupled to the normal derivative at the boundary. Actually such a field has been proposed in the literature for different reasons, but its full impact never seems …
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