arXiv subjects

Taejin Lee

Publications and source records attributed to Taejin Lee.

At least 19 recordsLinked to original sources

arXiv2023

Audio coding with unified noise shaping and phase contrast control

Over the past decade, audio coding technology has seen standardization and the development of many frameworks incorporated with linear predictive coding (LPC). As LPC reduces information in the frequency domain, LP-based frequency-domain noise-shaping (FDNS) was previously proposed. To code transient signals effectively, FDNS with temporal noise shaping (TNS) has emerged. However, these mainly operated in the modified discrete cosine transform domain, which essentially accompanies time domain aliasing. In this paper, a unified noise-shaping (UNS) framework including FDNS and complex LPC-based TNS (CTNS) in the DFT domain is proposed to overcome the aliasing issues. Additionally, a modified polar quantizer with phase contrast control is proposed, which saves phase bits depending on the frequency envelope information. The core coding feasibility at low bit rates is verified through various objective metrics and subjective listening evaluations.

eess.AS↗

arXiv2022

BRST Ghost-Vertex Operator in Witten's Cubic Open String Field Theory on Multiple $Dp$-branes

The Becchi-Rouet-Stora-Tyutin (BRST) ghost field is a key element in constructing Witten's cubic open string field theory. However, to date, the ghost sector of the string field theory has not received a great deal of attention. In this study, we address the BRST ghost on multiple $Dp$-branes, which carries non-Abelian indices and couples to a non-Ablelian gauge field. We found that the massless components of the BRST ghost field can play the role of the Faddeev-Popov ghost in the non-Alelian gauge field, such that the string field theory maintains the local non-Abelian gauge invariance.

hep-th↗

arXiv2022

NSR Open Super-string in the proper-time gauge I: Free Field Theory

We study the Neveu-Schwarz-Ramond (NSR) open super-string theory in the proper-time gauge. The string field action is obtained by evaluating the Polyakov string path integral. In this study, we focus on the open-string free-field action, which corresponds to the string path integral on a strip. Depending on the periodicity of the fermion fields, the open super-string has two sectors: The Neveu-Schwarz (NS) and Ramond (R) sectors. We can impose the gauge conditions to fix the (super-) reparametrization invariance on the two-dimensional metric and its super-partner on the string world sheet to secure the covariance, in contrast to the light-cone gauge condition. Accordingly, the proper-time emerges in the NS sector and both proper-time and its super-partner appear in the R-sector. Integration leads to free-string field actions in both sectors.

hep-th↗

arXiv2022

Witten's Cubic Open String Field Theory on multiple $Dp$-branes

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 cubic interaction reduces correctly to the cubic term of the non-Abelian gauge fields, cubic interaction terms of the gauge fields, and the scalar fields on $(p+1)$ dimensional space. Thus, Witten's string field theory may be a useful tool to study the quantum dynamics of open strings on multiple $Dp$-branes.

hep-th↗

arXiv2022

Cubic Closed String Field Theory on a Double Layer

Various studies have attempted to extend the Witten's cubic open string field theory to the cubic closed string field theory, which may describe Einstein gravity in the low energy sector consistently. In the present study we propose a cubic closed string field theory, introducing a double layer to describe the closed string world-sheet as an extension of the open string world-sheet of the Witten's cubic open string. We mapped the closed string world-sheet onto the complex plane, of which the lower half plane is completely covered by the extended part of the string world-sheet. Using the Green's function on the complex plane, evaluated the Polyakov string path integral, from which we extracted the Neumann functions and the vertex operators. We obtained the one and two string vertices (identities) following this procedure and finally the cubic string vertex operator. It is notable that the obtained cubic string scattering amplitude coincide with the cubic graviton interaction of the Einstein gravity. Thus, the resultant cubic closed string field theory consistently describes the Einstein gravity. We also show that the Kawai-Lewellen-Tye (KLT) relations of the first quantized string theory may be manifested in the cubic closed string field theory.

hep-th↗

arXiv2020

Canonical Quantization of Massive Symmetric Rank-Two Tensor in String Theory

The canonical quantization of a massive symmetric rank-two tensor in string theory, which contains two Stueckelberg fields, was studied. As a preliminary study, we performed a canonical quantization of the Proca model to describe a massive vector particle that shares common properties with the massive symmetric rank-two tensor model. By performing a canonical analysis of the Lagrangian, which describes the symmetric rank-two tensor, obtained by Siegel and Zwiebach (SZ) from string field theory, we deduced that the Lagrangian possesses only first class constraints that generate local gauge transformation. By explicit calculations, we show that the massive symmetric rank-two tensor theory is gauge invariant only in the critical dimension of open bosonic string theory, i.e., $d=26$. This emphasizes that the origin of local symmetry is the nilpotency of the Becchi-Rouet-Stora-Tyutin (BRST) operator, which is valid only in the critical dimension. For a particular gauge imposed on the Stueckelberg fields, the gauge-invariant Lagrangian of the SZ model reduces to the Fierz-Pauli Lagrangian of a massive spin-two particle. Thus, the Fierz-Pauli Lagrangian is a gauge-fixed version of the gauge-invariant Lagrangian for a massive symmetric rank-two tensor. By noting that the Fierz-Pauli Lagrangian is not suitable for studying massive spin-two particles with small masses, we propose the transverse-traceless (TT) gauge to quantize the SZ model as an alternative gauge condition. In the TT gauge, the two Stueckelberg fields can be decoupled from the symmetric rank-two tensor and integrated trivially. The massive spin-two particle can be described by the SZ model in the TT gauge, where the propagator of the massive spin-two particle has a well-defined massless limit.

hep-th↗

arXiv2019

Graviton and Massive Symmetric Rank-Two Tensor in String Theory

Spin-two particles appear in the spectra of both open and closed string theories. We studied a graviton and massive symmetric rank-two tensor in string theory, both of which carry spin two. A graviton is a massless spin-two particle in closed string theory while a symmetric rank-two tensor is a massive particle with spin two in open string theory. Using Polyakov's string path integral formulation of string scattering amplitudes, we calculated cubic interactions of both spin-two particles explicitly, including $\ap$-corrections (string corrections). We observed that the cubic interactions of the massive spin-two particle differed from those of the graviton. The massive symmetric rank-two tensor in open string theory becomes massless in the high energy limit where $\ap \rightarrow \infty$ and $\ap$-correction terms, containing higher derivatives, dominate: In this limit the local cubic action of the symmetric rank-two tensor of open string theory coincides with that of the graviton in closed string theory.

hep-th↗

arXiv2019

Saving Tachyons in Open String Theory

Using string scattering amplitudes of open bosonic string on a single $D$-brane, we construct a local field theoretical action for tachyon fields. Cubic local interactions between various particles, belonging to the particle spectrum of string may be directly followed from three-string scattering amplitude. These cubic local interactions may generate perturbative non-local four-particle interactions, which may contribute to four-string scattering amplitude. It was observed that tachyon field in open bosonic string theory must be represented by a complex field in order to reproduce the Veneziano amplitude, describing four-tachyon scattering. The Veneziano amplitude, expanded in terms of $s$-channel poles was compared with the four-tachyon scattering amplitudes in $s$-channel generated perturbatively and it was found that a quartic potential term is needed in the local field theoretical action, which describes open string theory effectively in the low energy regime. With this quartic term, the tachyon potential has a stable minimum point and the tachyon field may condensate. As a result, both tachyon and gauge fields become massive at Planck scale and completely disappear from the low energy particle spectrum.

hep-th↗

arXiv2019

Four-Graviton Scattering and String Path Integral in the Proper-time gauge

We evaluate the four-closed-string scattering amplitude, using the Polyakov string path integral in the proper-time gauge. By identifying the Fock space representation of the four-closed-string-vertex, we obtain a field theoretic expression of the closed string scattering amplitudes. In the zero-slope limit, the four-closed-string scattering amplitude reduces to the four-graviton-scattering amplitude of Einstein's gravity. However, at a finite slope, the four-graviton scattering amplitude in the proper-time gauge differs not only from that of Einstein gravity, but also significantly differs from the conventional one obtained by using the vertex operator technique in string theory. This discrepancy is mainly due to the presence of closed string tachyon poles in the four-graviton-scattering amplitude, which are missing in previous works. Because the tachyon poles in the scattering amplitude considerably alter the short distance behavior of gravitational interaction, they may be important in understanding problems associated with the perturbative theory of quantum gravity and the dark matter within the framework of string theory.

hep-th↗

arXiv2019

Four-Gauge-Particle Scattering Amplitudes and Polyakov String Path Integral in the proper-time gauge

We evaluate four-gauge-particle tree level scattering amplitudes using the Polyakov string path integral in the proper-time gauge, where the string path integral can be cast into the Feynman-Schwinger proper-time representation. We compare the resultant scattering amplitudes, which include $\ap$-corrections, with the conventional ones that may be obtained by substituting local vertex operators for the external string states. In the zero-slope limit, both amplitudes are reduced to the four-gauge-particle scattering amplitude of non-Abelian Yang-Mills gauge theory. However, when the string corrections become relevant with finite $\ap$, the scattering amplitude in the proper-time gauge differs from the conventional one: The Polyakov string path integral in the proper-time gauge, equivalent to the deformed cubic string field theory, systematically provides the alpha prime corrections. In addition, we find that the scattering amplitude in the proper-time gauge contains tachyon poles in a manner consistent with three-particle-scattering amplitudes. The scattering amplitudes evaluated using the Polyakov string path integral in the proper-time gauge may be more suitable than conventional ones for exploring string corrections to the quantum field theories and high energy behaviors of open string.

hep-th↗

arXiv2018

Covariant Open String Field Theory on Multiple $Dp$-Branes

We study covariant open bosonic string field theories on multiple $Dp$-branes by using the deformed cubic string field theory which is equivalent to the string field theory in the proper-time gauge. Constructing the Fock space representations of the three-string vertex and the four-string vertex on multiple $Dp$-branes, we obtain the field theoretical effective action in the zero-slope limit. On the multiple $D0$-branes, the effective action reduces to the Banks-Fishler-Shenker-Susskind (BFSS) matrix model. We also discuss the relation between the open string field theory on multiple $D$-instantons in the zero-slope limit and the Ishibashi-Kawai-Kitazawa-Tsuchiya (IKKT) matrix model. The covariant open string field theory on multiple $Dp$-branes would be useful to study the non-perturbative properties of quantum field theories in $(p+1)$-dimensions in the framework of the string theory. The non-zero-slope corrections may be evaluated systematically by using the covariant string field theory.

hep-th↗

arXiv2018

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 $2 \le p \le d_{\text{critical}} -2$ and logarithmically divergent for $p =1, d_{\text{critical}}-1$.

hep-th↗

arXiv2017

String Scattering Amplitudes and Deformed Cubic String Field Theory

We study string scattering amplitudes by using the deformed cubic string field theory which is equivalent to the string field theory in the proper-time gauge. The four-string scattering amplitudes with three tachyons and an arbitrary string state are calculated. The string field theory yields the string scattering amplitudes evaluated on the world sheet of string scattering whereas the coventional method, based on the first quantized theory brings us the string scattering amplitudes defined on the upper half plane. For the highest spin states, generated by the primary operators, both calculations are in perfect agreement. In this case, the string scattering amplitudes are invariant under the conformal transformation, which maps the string world sheet onto the upper half plane. If the external string states are general massive states, generated by non-primary field operators, we need to take into account carefully the conformal transformation between the world sheet and the upper half plane. We show by an explicit calculation that the string scattering amplitudes calculated by using the deformed cubic string field theory transform into those of the first quantized theory on the upper half plane by the conformal transformation, generated by the Schwarz-Christoffel mapping.

hep-th↗

arXiv2017

Gravitational Scattering Amplitudes and Closed String Field Theory in the Proper-Time Gauge

We construct a covariant closed string field theory by extending recent works on the covariant open string field theory in the proper-time gauge. Rewriting the string scattering amplitudes generated by the closed string field theory in terms of the Polyakov string path integrals, we identify the Fock space representations of the closed string vertices. We show that the Fock space representations of the closed string field theory may be completely factorized into those of the open string field theory. It implies that the well known Kawai-Lewellen-Tye (KLT) relations of the first quantized string theory may be promoted to the second quantized closed string theory. We explicitly calculate the scattering amplitudes of three gravitons by using the closed string field theory in the proper-time gauge.

hep-th↗

arXiv2017

Solving Lauricella String Scattering Amplitudes through Recurrence Relations

We show that there exist infinite number of recurrence relations valid for all energies among the open bosonic string scattering amplitudes (SSA) of three tachyons and one arbitrary string state, or the Lauricella SSA. Moreover, these infinite number of recurrence relations can be used to solve all the Lauricella SSA and express them in terms of one single four tachyon amplitude. These results extend the solvability of SSA at the high energy, fixed angle scattering limit and those at the Regge scattering limit discovered previously.

hep-th↗

arXiv2017

Covariant open bosonic string field theory on multiple D-branes in the proper-time gauge

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 to the Witten's cubic string field theory. Having obtained planar diagrams, we may adopt the light-cone string field theory technique to calculate the multi-string scattering amplitudes with an arbitrary number of external strings. We examine in detail the three-string vertex diagram and the effective four-string vertex diagrams generated perturbatively by the three-string vertex at tree level. In the zero-slope limit, the string scattering amplitudes are identified precisely as those of non-Abelian Yang-Mills gauge theory if the external states are chosen to be massless vector particles.

hep-th↗

arXiv2017

Deformation of the Cubic Open String Field Theory

We study a consistent deformation of the cubic open bosonic string theory in such a way that the non-planar world sheet diagrams of the perturbative string theory are mapped onto their equivalent planar diagrams of the light-cone string field theory with some length parameters fixed. An explicit evaluation of the cubic string vertex in the zero-slope limit yields the correct relationship between the string coupling constant and the Yang-Mills coupling constant. The deformed cubic open string field theory is shown to produce the non-Abelian Yang-Mills action in the zero-slope limit if it is defined on multiple D-branes. Applying the consistent deformation systematically to multi-string world sheet diagrams, we may be able to calculate scattering amplitudes with an arbitrary number of external open strings.

hep-th↗

arXiv2016

Hetero-Junction of Two Quantum Wires: Critical Line and Duality

Applying the Fermi-Bose equivalence and the boundary state formulation, we study the hetero-junction of two quantum wires. Two quantum wires are described by Tomonaga-Luttinger (TL) liquids with different TL parameters and electrons transport between two wires is depicted by a simple hopping interaction. We calculate the radiative corrections to the hopping interaction and obtain the renormalization (RG) exponent, making use of the perturbation theory based on the boundary state formulation. The model exhibits a phase transition at zero temperature. We discuss the critical line which defines the phase boundary on the two dimensional parameter space. The model also exhibits the particle-kink duality, which maps the strong coupling regime of the model onto the weak coupling regime of the dual model. The strong coupling regime of the model is found to match exactly the weak coupling regime of the dual model. This model is also important to study the critical behaviors of the two dimensional dissipative system with anisotropic friction coefficients.

cond-mat.str-el↗