arXiv subjects

Sung-Kil Yang

Publications and source records attributed to Sung-Kil Yang.

At least 19 recordsLinked to original sources

arXiv2001

ADE Singularities and Coset Models

We consider the compactification of the IIA string to (1+1) dimensions on non-compact 4-folds that are ALE fibrations. Supersymmetry requires that the compactification include 4-form fluxes, and a particular class of these models has been argued by Gukov, Vafa and Witten to give rise to a set of perturbed superconformal coset models that also have a Landau-Ginzburg description. We examine all these ADE models in detail, including the exceptional cosets. We identify which perturbations are induced by the deformation of the singularity, and compute the Landau-Ginzburg potentials exactly. We also show how the the Landau-Ginzburg fields and their superpotentials arise from the geometric data of the singularity, and we find that this is most naturally described in terms of non-compact, holomorphic 4-cycles.

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arXiv2000

Duality Between String Junctions and D-Branes on Del Pezzo Surfaces

We revisit local mirror symmetry associated with del Pezzo surfaces in Calabi-Yau threefolds in view of five-dimensional N=1 E_N theories compactified on a circle. The mirror partner of singular Calabi-Yau with a shrinking del Pezzo four-cycle is described as the affine 7-brane backgrounds probed by a D3-brane. Evaluating the mirror map and the BPS central charge we relate junction charges to RR charges of D-branes wrapped on del Pezzo surfaces. This enables us to determine how the string junctions are mapped to D-branes on del Pezzo surfaces.

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arXiv2000

Closed Sub-Monodromy Problems, Local Mirror Symmetry and Branes on Orbifolds

We study D-branes wrapping an exceptional four-cycle P(1,a,b) in a blown-up C^3/Z_m non-compact Calabi-Yau threefold with (m;a,b)=(3;1,1), (4;1,2) and (6;2,3). In applying the method of local mirror symmetry we find that the Picard-Fuchs equations for the local mirror periods in the Z_{3,4,6} orbifolds take the same form as the ones in the local E_{6,7,8} del Pezzo models, respectively. It is observed, however, that the orbifold models and the del Pezzo models possess different physical properties because the background NS B-field is turned on in the case of Z_{3,4,6} orbifolds. This is shown by analyzing the periods and their monodromies in full detail with the help of Meijer G-functions. We use the results to discuss D-brane configurations on P(1,a,b) as well as on del Pezzo surfaces. We also discuss the number theoretic aspect of local mirror symmetry and observe that the exponent which governs the exponential growth of the Gromov-Witten invariants is determined by the special value of the Dirichlet L-function.

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arXiv1999

Mordell-Weil Lattice via String Junctions

We analyze the structure of singularities, Mordell-Weil lattices and torsions of a rational elliptic surface using string junctions in the background of 12 7-branes. The classification of the Mordell-Weil lattices due to Oguiso-Shioda is reproduced in terms of the junction lattice. In this analysis an important role played by the global structure of the surface is observed. It is then found that the torsions in the Mordell-Weil group are generated by the fraction of loop junctions which represent the imaginary roots of the loop algebra $\hat E_9$. From the structure of the Mordell-Weil lattice we find 7-brane configurations which support non-BPS junctions carrying conserved Abelian charges.

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arXiv1999

Affine 7-brane Backgrounds and Five-Dimensional $E_N$ Theories on $S^1$

Elliptic curves for the 7-brane configurations realizing the affine Lie algebras $\wh E_n$ $(1 \leq n \leq 8)$ and $\wh{\wt E}_n$ $(n=0,1)$ are systematically derived from the cubic equation for a rational elliptic surface. It is then shown that the $\wh E_n$ 7-branes describe the discriminant locus of the elliptic curves for five-dimensional (5D) N=1 $E_n$ theories compactified on a circle. This is in accordance with a recent construction of 5D N=1 $E_n$ theories on the IIB 5-brane web with 7-branes, and indicates the validity of the D3 probe picture for 5D $E_n$ theories on $\bR^4 \times S^1$. Using the $\wh E_n$ curves we also study the compactification of 5D $E_n$ theories to four dimensions.

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arXiv1999

N=2 Superconformal Field Theory with ADE Global Symmetry on a D3-brane Probe

We study mass deformations of N=2 superconformal field theories with ADE global symmetries on a D3-brane. The N=2 Seiberg-Witten curves with ADE symmetries are determined by the Type IIB 7-brane backgrounds which are probed by a D3-brane. The Seiberg-Witten differentials $λ$ for these ADE theories are constructed. We show that the poles of $λ$ with residues are located on the global sections of the bundle in an elliptic fibration. It is then clearly seen how the residues transform in an irreducible representation of the ADE groups. The explicit form of $λ$ depends on the choice of a representation of the residues. Nevertheless the physics results are identical irrespective of the representation of $λ$. This is considered as the global symmetry version of the universality found in N=2 Yang-Mills theory with local ADE gauge symmetries.

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arXiv1998

Seiberg-Witten Geometry with Various Matter Contents

We obtain the Seiberg-Witten geometry for four-dimensional N=2 gauge theory with gauge group SO(2N_c) (N_c \leq 5) with massive spinor and vector hypermultiplets by considering the gauge symmetry breaking in the N=2 $E_6$ theory with massive fundamental hypermultiplets. In a similar way the Seiberg-Witten geometry is determined for N=2 SU(N_c) (N_c \leq 6) gauge theory with massive antisymmetric and fundamental hypermultiplets. Whenever possible we compare our results expressed in the form of ALE fibrations with those obtained by geometric engineering and brane dynamics, and find a remarkable agreement. We also show that these results are reproduced by using N=1 confining phase superpotentials.

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arXiv1998

Seiberg-Witten Theory as d<1 Topological Strings

In view of two-dimensional topological gravity coupled to matter, we study the Seiberg-Witten theory for the low-energy behavior of N=2 supersymmetric Yang-Mills theory with ADE gauge groups. We construct a new solution of the Picard-Fuchs equations obeyed by the Seiberg-Witten periods. Our solution is expressed as the linear sum over the infinite set of one-point functions of gravitational descendants in $d<1$ topological strings. It turns out that our solution provides the power series expansion around the origin of the quantum moduli space of the Coulomb branch. For SU(N) gauge group we show how the Seiberg-Witten periods are reconstructed from the present solution.

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arXiv1998

The WDVV Equations in N=2 Supersymmetric Yang-Mills Theory

We present a simple proof of the WDVV equations for the prepotential of four-dimensional N=2 supersymmetric Yang-Mills theory with all ADE gauge groups. According to our proof it is clearly seen that the WDVV equations in four dimensions have their origin in the associativity of the chiral ring in two-dimensional topological Landau-Ginzburg models. The WDVV equations for the BC gauge groups are also studied in the Landau-Ginzburg framework. We speculate about the topological field theoretic interpretation of the Seiberg-Witten solution of N=2 Yang-Mills theory.

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arXiv1998

Donaldson-Witten Functions of Massless N=2 Supersymmetric QCD

We study the Donaldson-Witten function in four-dimensional topological gauge theory which is constructed from N=2 supersymmetric SU(2) gauge theory with $N_f < 4$ massless fundamental hypermultiplets. When $N_f = 2,3$, the strong-coupling singularities with multiple massless monopoles appear in the moduli space (the u-plane) of the Coulomb branch. We show that the invariants made out of such singularities exhibit a property which is similar to the one expected for four-manifolds of generalized simple type.

hep-th↗

arXiv1998

A-D-E Singularity and Prepotentials in N=2 Supersymmetric Yang-Mills Theory

We calculate the instanton corrections in the effective prepotential for N=2 supersymmetric Yang-Mills theory with all A-D-E gauge groups from the Seiberg-Witten geometry constructed out of the spectral curves of the affine Toda lattice. The one-instanton contribution is determined explicitly by solving the Gauss-Manin system associated with the A-D-E singularity. Our results are in complete agreement with the ones obtained from the microscopic instanton calculations.

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arXiv1998

Exceptional Seiberg-Witten Geometry with Massive Fundamental Matters

We propose Seiberg-Witten geometry for N=2 gauge theory with gauge group $E_6$ with massive $N_f$ fundamental hypermultiplets. The relevant manifold is described as a fibration of the ALE space of $E_6$ type. It is observed that the fibering data over the base ${\bf CP}^1$ has an intricate dependence on hypermultiplet bare masses.

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arXiv1997

Flat Coordinates, Topological Landau-Ginzburg Models and the Seiberg-Witten Period Integrals

We study the Picard-Fuchs differential equations for the Seiberg-Witten period integrals in N=2 supersymmetric Yang-Mills theory. For A-D-E gauge groups we derive the Picard-Fuchs equations by using the flat coordinates in the A-D-E singularity theory. We then find that these are equivalent to the Gauss-Manin system for two-dimensional A-D-E topological Landau-Ginzburg models and the scaling relation for the Seiberg-Witten differential. This suggests an interesting relationship between four-dimensional N=2 gauge theories in the Coulomb branch and two-dimensional topological field theories.

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arXiv1997

ADE Confining Phase Superpotentials

We obtain a low-energy effective superpotential for a phase with a single confined photon in N=1 gauge theory with an adjoint matter with ADE gauge groups. The expectation values of gauge invariants built out of the adjoint field parametrize the singularities of moduli space of the Coulomb phase. The result can be used to derive the N=2 curve in the form of a foliation over $CP^1$. Our N=1 theory exhibits non-trivial fixed points which naturally inherit the properties of the ADE classification of N=2 superconformal field theories in four dimensions. We also discuss how to include matter hypermultiplets toward deriving the Riemann surface which describes N=2 QCD with exceptional gauge groups.

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arXiv1996

A New Description of the E_6 Singularity

We discuss a new type of Landau-Ginzburg potential for the E_6 singularity of the form $W=const+(Q_1(x)+P_1(x)\sqrt{P_2(x)})/x^3$ which featured in a recent study of heterotic/typeII string duality. Here $Q_1,P_1$ and $P_2$ are polynomials of degree 15,10 and 10, respectively. We study the properties of the potential in detail and show that it gives a new and consistent description of the E_6 singularity.

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arXiv1996

Confining Phase of N=1 Supersymmetric Gauge Theories and N=2 Massless Solitons

Effective superpotentials for the phase with a confined photon are obtained in $N=1$ supersymmetric gauge theories. We use the results to derive the hyperelliptic curves which describe the Coulomb phase of $N=2$ theories with classical gauge groups, and thus extending the prior result for $SU(N_c)$ gauge theory by Elitzur et al. Moreover, adjusting the coupling constants in $N=1$ effective superpotentials to the values of $N=2$ non-trivial critical points we find new classes of $N=1$ superconformal field theories with an adjoint matter with a superpotential.

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arXiv1996

Picard-Fuchs Equations and Prepotentials in $N=2$ Supersymmetric QCD

The Picard-Fuchs equations for $N=2$ supersymmetric $SU(N_{c})$ Yang-Mills theories with massless hypermultiplets are obtained for $N_{c}=2$ and $3$. For $SU(2)$ we derive the non-linear differential equations for the prepotentials and calculate full non-perturbative corrections to the effective gauge coupling constant in the weak and strong coupling regions.

hep-th↗

arXiv1996

Study of $N=2$ Superconformal Field Theories in $4$ Dimensions

Making use of the exact solutions of the $N=2$ supersymmetric gauge theories we construct new classes of superconformal field theories (SCFTs) by fine-tuning the moduli parameters and bringing the theories to critical points. SCFTs we have constructed represent universality classes of the 4-dimensional $N=2$ SCFTs.

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