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Ta-Sheng Tai

Publications and source records attributed to Ta-Sheng Tai.

At least 19 recordsLinked to original sources
arXiv2012

On non-stationary Lamé equation from WZW model and spin-1/2 XYZ chain

We study the link between WZW model and the spin-1/2 XYZ chain. This is achieved by comparing the second-order differential equations from them. In the former case, the equation is the Ward-Takahashi identity satisfied by one-point toric conformal blocks. In the latter case, it arises from Baxter's TQ relation. We find that the dimension of the representation space w.r.t. the V-valued primary field in these conformal blocks gets mapped to the total number of chain sites. By doing so, Stroganov's "The Importance of being Odd" (cond-mat/0012035) can be consistently understood in terms of WZW model language. We first confirm this correspondence by taking a trigonometric limit of the XYZ chain. That eigenstates of the resultant two-body Sutherland model from Baxter's TQ relation can be obtained by deforming toric conformal blocks supports our proposal.

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arXiv2012

R**2 correction to BMPV black hole entropy from Kerr/CFT correspondence

Following Kerr/CFT correspondence, we compute the entropy of five-dimensional supersymmetric rotating BMPV black holes.We successfully reproduce Iyer-Wald formula in the presence of Gauss-Bonnet terms from the viewpoint of microscopic CFT. This further supports the higher-derivative version of Kerr/CFT prescription proposed in arXiv:0903.4176 for four-dimensional extremal Kerr black holes.

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arXiv2011

Baxter's T-Q equation, SU(N)/SU(2)^{N-3} correspondence and Ω-deformed Seiberg-Witten prepotential

We study Baxter's T-Q equation of XXX spin-chain models under the semiclassical limit where an intriguing SU(N)/SU(2)^{N-3} correspondence emerges. That is, two kinds of 4D \mathcal{N}=2 superconformal field theories having the above different gauge groups are encoded simultaneously in one Baxter's T-Q equation which captures their spectral curves. For example, while one is SU(N_c) with N_f=2N_c flavors the other turns out to be SU(2)^{N_c-3} with N_c hyper-multiplets (N_c > 3). It is seen that the corresponding Seiberg-Witten differential supports our proposal.

hep-th↗
arXiv2011

Uniformization, Calogero-Moser/Heun duality and Sutherland/bubbling pants

Inspired by the work of Alday, Gaiotto and Tachikawa (AGT), we saw the revival of Poincar{é}'s uniformization problem and Fuchsian equations obtained thereof. Three distinguished aspects are possessed by Fuchsian equations. First, they are available via imposing a classical Liouville limit on level-two null-vector conditions. Second, they fall into some A_1-type integrable systems. Third, the stress-tensor present there (in terms of the Q-form) manifests itself as a kind of one-dimensional "curve". Thereby, a contact with the recently proposed Nekrasov-Shatashvili limit was soon made on the one hand, whilst the seemingly mysterious derivation of Seiberg-Witten prepotentials from integrable models become resolved on the other hand. Moreover, AGT conjecture can just be regarded as a quantum version of the previous Poincar{é}'s approach. Equipped with these observations, we examined relations between spheric and toric (classical) conformal blocks via Calogero-Moser/Heun duality. Besides, as Sutherland model is also obtainable from Calogero-Moser by pinching tori at one point, we tried to understand its eigenstates from the viewpoint of toric diagrams with possibly many surface operators (toric branes) inserted. A picture called "bubbling pants" then emerged and reproduced well-known results of the non-critical self-dual c=1 string theory under a "blown-down" limit.

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arXiv2011

Triality in SU(2) Seiberg-Witten theory and Gauss hypergeometric function

Through AGT conjecture, we show how triality observed in \N=2 SU(2) N_f=4 QCD can be interpreted geometrically as the interplay among six of Kummer's twenty-four solutions belonging to one fixed Riemann scheme in the context of hypergeometric differential equations. We also stress that our presentation is different from the usual crossing symmetry of Liouville conformal blocks, which is described by the connection coefficient in the case of hypergeometric functions. Besides, upon solving hypergeometric differential equations at the zeroth order by means of the WKB method, a curve (thrice-punctured Riemann sphere) emerges. The permutation between these six Kummer's solutions then boils down to the outer automorphism of the associated curve.

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arXiv2010

New Gauged Linear Sigma Models for 8D HyperKahler Manifolds and Calabi-Yau Crystals

We propose two kinds of gauged linear sigma models whose moduli spaces are real eight-dimensional hyperKahler and Calabi-Yau manifolds, respectively. Here, hyperKahler manifolds have sp(2) holonomy in general and are dual to Type IIB (p,q)5-brane configurations. On the other hand, Calabi-Yau fourfolds are toric varieties expressed as quotient spaces. Our model involving fourfolds is different from the usual one which is directly related to a symplectic quotient procedure. Remarkable features in newly-found three-dimensional Chern-Simons-matter theories appear here as well, such as dynamical Fayet-Iliopoulos parameters, one dualized photon and its residual discrete gauge symmetry.

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arXiv2009

Eschenburg space as gravity dual of flavored N=4 Chern-Simons-matter theory

We find 3D flavored N=4 Chern-Simons-matter theory, a kind of N=3 SCFT, has a gravity dual AdS4xM7(t1,t2,t3) where three coprime parameters can be read off according to the number and charge of 5-branes in Type IIB setup. Because M7(t1,t2,t3) has been known in literatures as Eschenburg space, we exploit some of its properties to examine the correspondence between two sides.

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arXiv2009

Toward a Proof of Montonen-Olive Duality via Multiple M2-branes

We derive 4-dimensional N=4 U(N) supersymmetric Yang-Mills theory from a 3-dimensional Chern-Simons-matter theory with product gauge group U(N)^{2n}. The latter describes M2-branes probing an orbifold where a torus emerges in a scaling limit. It is expected that the SL(2, Z) duality of the 4-dimensional Yang-Mills theory will be shown in M-theory point of view since it is trivially realized as modular transformations of the torus. Indeed, starting from one single Chern-Simons-matter theory, we find infinitely many equivalent 4-dimensional theories differing up to T-transformation of the SL(2, Z) redefinition of the gauge coupling tau=theta/2pi + 4pi i/g^2 and a parity transformation in 4 dimensions. Although S-transformation can not be shown in our work, it is important that a part of the SL(2, Z) transformation is realized via the M2-brane action. Thus we think our work can be a step toward a proof of Montonen-Olive duality via M2-branes.

hep-th↗
arXiv2009

Kerr/CFT correspondence and five-dimensional BMPV black holes

We apply a recently proposed Kerr/CFT correspondence to extremal supersymmetric five-dimensional charged spinning black holes, constructed by Breckenridge, Myers, Peet and Vafa. By computing the central charge of the dual CFT and Frolov-Thorne temperature, Cardy's formula succeeds in reproducing Bekenstein-Hawking area law.

hep-th↗
arXiv2008

Extended MQCD and SUSY/non-SUSY duality

We study the SUSY/non-SUSY duality proposed by Aganagic et al. from Type IIA string and M-theory perspectives. We find that our brane configuration generalizes the so-called $extended$ Seiberg-Witten theory on the one hand, and provides a way to realize non-SUSY vacua by intersecting NS5-branes on the other hand. We also argue how the partial SUSY breaking from $\Ncal=2$ down to $\Ncal=1$ can be clearly visualized through the brane picture.

hep-th↗
arXiv2007

Instanton Counting and Matrix Model

We construct an Imbimbo-Mukhi type matrix model, which reproduces exactly the partition function of ${\mathbb{CP}^1}$ topological strings in the small phase space, Nekrasov's instanton counting in ${\cal{N}}=2$ gauge theory and the large $N$ limit of the partition function in 2-dimensional Yang-Mills theory on a sphere. In addition, we propose a dual Stieltjes-Wigert type matrix model, which emerges when all-genus topological string amplitudes on certain simple toric Calabi-Yau manifolds are compared with the Imbimbo-Mukhi type model.

hep-th↗
arXiv2007

Two Polyakov Loop Correlators from D5-branes at Finite Temperature

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.}

hep-th↗
arXiv2007

Classical c=1 Tachyon Scattering and 1/2-BPS Correlators

We study the correlator of chiral primary operators in $\Ncal$=4 super Yang-Mills theory in large $N$ limit. Through the free fermion picture, we map the gauge group rank and R-charges in SYM to the Fermi level and tachyon momenta, respectively, in the c=1 matrix model. By doing so, it is seen that half-BPS correlators are reproduced by tree-level tachyon scattering amplitudes.

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arXiv2007

Correlator of Fundamental and Anti-symmetric Wilson Loops in AdS/CFT Correspondence

We study the two circular Wilson loop correlator in which one is of anti-symmetric representation, while the other is of fundamental representation in 4-dimensional ${\cal N}=4$ super Yang-Mills theory. This correlator has a good AdS dual, which is a system of a D5-brane and a fundamental string. We calculated the on-shell action of the string, and clarified the Gross-Ooguri transition in this correlator. Some limiting cases are also examined.

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arXiv2007

D-branes in the Lorentzian Melvin Geometry

We consider string theory on the Lorentzian Melvin geometry, which is obtained by analytically continuing the two-parameter Euclidean Melvin background. Because this model provides a solvable conformal field theory that describes time-dependent twisted string dynamics, we study the string one-loop partition function and the D-brane spectrum. We found that both the wrapping D2-brane and the codimension-one D-string emit winding strings, and this behavior can be traced to the modified open string Hamiltonian on these probe D-branes.

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arXiv2006

Winding String Dynamics in a Time-Dependent Beta Deformed Background

We study string theory on the analytically continued $β$ deformed background proposed in hep-th/0509036. This non-static model provides a solvable conformal field theory which describes time-dependent twisted string dynamics. With the mini-superspace approach, we examine disk one-point correlators of D-branes and compute the winding string pair production rate. We find that these results are consistent with the CFT computation.

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