arXiv subjects

Changhyun Ahn

Publications and source records attributed to Changhyun Ahn.

At least 109 records · Page 6Linked to original sources

arXiv2004

Supersymmetric Gauge Theories with Flavors and Matrix Models

We present two results concerning the relation between poles and cuts by using the example of N=1 U(N_c) gauge theories with matter fields in the adjoint, fundamental and anti-fundamental representations. The first result is the on-shell possibility of poles, which are associated with flavors and on the second sheet of the Riemann surface, passing through the branch cut and getting to the first sheet. The second result is the generalization of hep-th/0311181 (Intriligator, Kraus, Ryzhov, Shigemori, and Vafa) to include flavors. We clarify when there are closed cuts and how to reproduce the results of the strong coupling analysis by matrix model, by setting the glueball field to zero from the beginning. We also make remarks on the possible stringy explanations of the results and on generalization to SO(N_c) and USp(2N_c) gauge groups.

hep-th↗

arXiv2004

More on N=1 Matrix Model Curve for Arbitrary N

Using both the matrix model prescription and the strong-coupling approach, we describe the intersections of n=0 and n=1 non-degenerated branches for quartic (polynomial of adjoint matter) tree-level superpotential in N=1 supersymmetric SO(N)/USp(2N) gauge theories with massless flavors. We also apply the method to the degenerated branch. The general matrix model curve on the two cases we obtain is valid for arbitrary N and extends the previous work from strong-coupling approach. For SO(N) gauge theory with equal massive flavors, we also obtain the matrix model curve on the degenerated branch for arbitrary N. Finally we discuss on the intersections of n=0 and n=1 non-degenerated branches for equal massive flavors.

hep-th↗

arXiv2004

The Matrix Model Curve Near the Singularities

In N=1 supersymmetric SO(N)/USp(2N) gauge theories with the tree-level superpotential W(Φ) that is an arbitrary polynomial of the adjoint matter Φ, the massless fluctuations about each quantum vacuum are described by U(1)^n gauge theory. By turning on the parameters of W(Φ) to the special values, the singular vacua where the additional fields become massless can be reached. Using the matrix model prescription, we study the intersections of n=0 and n=1 branches. The general formula for the matrix model curve at the singularity which is valid for arbitrary N is obtained and this generalizes the previous results for small values of N from strong-coupling approach. Applying the analysis to the degenerated case, we also obtain a general matrix model curve which is not only valid at a special point but also on the whole branch.

hep-th↗

arXiv2003

Domain Wall from Gauged d=4, N=8 Supergravity: Part II

The scalar potentials of the non-semi-simple CSO(p,8-p)(p=7,6,5) gaugings of N=8 supergravity are studied for critical points. The CSO(7,1) gauging has no G_2-invariant critical points, the CSO(6,2) gauging has three new SU(3)-invariant AdS critical points and the CSO(5,3) gauging has no SO(5)-invariant critical points. The scalar potential of CSO(6,2) gauging in four dimensions we discovered provides the SU(3) invariant scalar potential of five dimensional SO(6) gauged supergravity. The nontrivial effective scalar potential can be written in terms of the superpotential which can be read off from A_1 tensor of the theory. We discuss first-order domain wall solutions by analyzing the supergravity scalar-gravity action and using some algebraic relations in a complex eigenvalue of A_1 tensor. We examine domain wall solutions of G_2 sectors of noncompact SO(7,1) and CSO(7,1) gaugings and SU(3) sectors of SO(6,2) and CSO(6,2) gaugings. They share common features with each sector of compact SO(8) gauged N=8 supergravity in four dimensions. We analyze the scalar potentials of the CSO(p,q,8-p-q) gauged supergravity we have found before. The CSO(p,6-p,2) gauge theory in four dimensions can be reduced from the SO(p,6-p) gauge theory in five dimensions. Moreover, the SO(p,5-p) gauge theory in seven dimensions reduces to CSO(p,5-p,3) gauge theory in four dimensions. Similarly, CSO(p,q-p,8-q) gauge theories in four dimensions are related to SO(p,q-p)(q=2,3,4,7) gauge theories in other dimensions.

hep-th↗

arXiv2003

Phases of N=1 USp(2N_c) Gauge Theories with Flavors

We studied the phase structures of N=1 supersymmetric USp(2N_c) gauge theory with N_f flavors in the fundamental representation as we deformed the N=2 supersymmetric QCD by adding the superpotential for adjoint chiral scalar field. We determined the most general factorization curves for various breaking patterns, for example, the two different breaking patterns of quartic superpotential. We observed all kinds of smooth transitions for quartic superpotential. Finally we discuss the intriguing role of USp(0) in the phase structure and the possible connection with observations made recently in hep-th/0304271 (Aganagic, Intriligator, Vafa and Warner) and in hep-th/0307063 (Cachazo).

hep-th↗

arXiv2003

Phases of N=1 SO(N_c) Gauge Theories with Flavors

We studied the phase structures of ${\cal N}=1$ supersymmetric $SO(N_c)$ gauge theory with $N_f$ flavors in the vector representation as we deformed the ${\cal N}=2$ supersymmetric QCD by adding the superpotential of arbitrary polynomial for the adjoint chiral scalar field. Using weak and strong coupling analyses, we determined the most general factorization forms for various breaking patterns. We observed all kinds of smooth transitions for quartic superpotential.

hep-th↗

arXiv2003

Phases of N=1 Supersymmetric SO/Sp Gauge Theories via Matrix Model

We extend the results of Cachazo, Seiberg and Witten to N=1 supersymmetric gauge theories with gauge groups SO(2N), SO(2N+1) and Sp(2N). By taking the superpotential which is an arbitrary polynomial of adjoint matter Φas a small perturbation of N=2 gauge theories, we examine the singular points preserving N=1 supersymmetry in the moduli space where mutually local monopoles become massless. We derive the matrix model complex curve for the whole range of the degree of perturbed superpotential. Then we determine a generalized Konishi anomaly equation implying the orientifold contribution. We turn to the multiplication map and the confinement index K and describe both Coulomb branch and confining branch. In particular, we construct a multiplication map from SO(2N+1) to SO(2KN-K+2) where K is an even integer as well as a multiplication map from SO(2N) to SO(2KN-2K+2) (K is a positive integer), a map from SO(2N+1) to SO(2KN-K+2) (K is an odd integer) and a map from Sp(2N) to Sp(2KN+2K-2). Finally we analyze some examples which show some duality: the same moduli space has two different semiclassical limits corresponding to distinct gauge groups.

hep-th↗

arXiv2003

Supersymmetric SO(N_c) Gauge Theory and Matrix Model

By applying the method of Dijkgraaf-Vafa, we study matrix model related to supersymmetric SO(N_c) gauge theory with N_f flavors of quarks in the vector representation found by Intriligator-Seiberg. By performing the matrix integral over tree level superpotential characterized by light meson fields (mass deformation) in electric theory, we reproduce the exact effective superpotential in the gauge theory side. Moreover, we do similar analysis in magnetic theory. It turns out the matrix descriptions of both electric and magnetic theories are the same: Seiberg duality in the gauge theory side.

hep-th↗

arXiv2003

N=2 Supersymmetric SO(N)/Sp(N) Gauge Theories from Matrix Model

We use the matrix model to describe the N=2 SO(N)/Sp(N) supersymmetric gauge theories with massive hypermultiplets in the fundamental representation. By taking the tree level superpotential perturbation made of a polynomial of a scalar chiral multiplet, the effective action for the eigenvalues of chiral multiplet can be obtained. By varying this action with respect to an eigenvalue, a loop equation is obtained. By analyzing this equation, we derive the Seiberg-Witten curve within the context of matrix model.

hep-th↗

arXiv2003

Supersymmetric SO(N)/Sp(N) Gauge Theory from Matrix Model:Exact Mesonic Vacua

By performing the matrix integral over the tree level superpotential of N=1 supersymmetric SO(N)/Sp(N) gauge theories obtained from N=2 SQCD by adding the mass term for the adjoint scalar field, the exact effective superpotential in terms of meson field contains the nonperturbative ADS superpotential as well as the classical tree level superpotential. By completing the meson matrix integral with the help of saddle point equation, we find the free energy contributions from matter part in terms of glueball field, the adjoint field mass and quark mass. By extremizing the effective superpotential with respect to the glueball field, we analyze the vacuum structure and describe the behavior of two limiting cases:zero limit of quark mass and infinity limit of adjoint field mass. We also study the magnetic theory.

hep-th↗

arXiv2002

Penrose Limit of AdS_4 x V_{5,2} and Operators with Large R Charge

We consider M-theory on AdS_4 x V_{5,2} where V_{5,2}= SO(5)/SO(3) is a Stiefel manifold. We construct a Penrose limit of AdS_4 x V_{5,2} that provides the pp-wave geometry. There exists a subsector of three dimensional N=2 dual gauge theory, by taking both the conformal dimension and R charge large with the finiteness of their difference, which has enhanced N=8 maximal supersymmetry. We identify operators in the N=2 gauge theory with supergravity KK excitations in the pp-wave geometry and describe how the gauge theory operators made out of chiral field of conformal dimension 1/3 fall into N=8 supermultiplets.

hep-th↗

arXiv2002

The 11-dimensional Metric for AdS/CFT RG Flows with Common SU(3) Invariance

The compact 7-manifold arising in the compactification of 11-dimensional supergravity is described by the metric encoded in the vacuum expectation values(vevs) in d=4, N=8 gauged supergravity. Especially, the space of SU(3)-singlet vevs contains various critical points and RG flows(domain walls) developing along AdS_4 radial coordinate. Based on the nonlinear metric ansatz of de Wit-Nicolai-Warner, we show the geometric construction of the compact 7-manifold metric and find the local frames(siebenbeins) by decoding the SU(3)-singlet vevs into squashing and stretching parameters of the 7-manifold. Then the 11-dimensional metric for the whole SU(3)-invariant sector is obtained as a warped product of an asymptotically AdS_4 space with a squashed and stretched 7-sphere. We also discuss the difference in the 7-manifold between two sectors, namely SU(3)xU(1)-invariant sector and G_2-invariant sector. In spite of the difference in base 6-sphere, both sectors share the 4-sphere of CP^2 associated with the common SU(3)-invariance of various 7-manifolds.

hep-th↗

arXiv2002

Penrose Limit of AdS_4 x N^{0,1,0} and N=3 Gauge Theory

We consider M-theory on AdS_4 x N^{0,1,0} where N^{0,1,0}= (SU(3) x SU(2))/(SU(2) x U(1)). We review a Penrose limit of AdS_4 x N^{0,1,0} that provides the pp-wave geometry of AdS_4 x S^7. There exists a subsector of three dimensional N=3 dual gauge theory, by taking both the conformal dimension and R-charge large with the finiteness of their difference, which has enhanced N=8 maximal supersymmetry. We identify operators in the N=3 gauge theory with supergravity KK excitations in the pp-wave geometry and describe how the N=2 gauge theory operators originating from both N=3 short vector multiplet and N=3 long gravitino multiplet fall into N=8 supermultiplets.

hep-th↗

arXiv2002

Comments on Penrose Limit of AdS_4 x M^{1,1,1}

We construct a Penrose limit of AdS_4 x M^{1,1,1} where M^{1,1,1}= SU(3) x SU(2) x U(1)/(SU(2) x U(1) x U(1)) that provides the pp-wave geometry equal to the one in the Penrose limit of AdS_4 x S^7. There exists a subsector of three dimensional N=2 dual gauge theory which has enhanced N=8 maximal supersymmetry. We identify operators in the N=2 gauge theory with supergravity KK excitations in the pp-wave geometry and describe how the gauge theory operators made out of two kinds of chiral fields of conformal dimension 4/9, 1/3 fall into N=8 supermultiplets.

hep-th↗

arXiv2002

More on Penrose Limit of AdS_4 x Q^{1,1,1}

We consider a Penrose limit of AdS_4 x Q^{1,1,1} that provides the pp-wave geometry equal to the one in the Penrose limit of AdS_4 x S^7. We expect that there exists a subsector of three dimensional N=2 dual gauge theory which has enhanced N=8 maximal supersymmetry. We identify operators in the N=2 gauge theory with 11-dimensional supergravity KK excitations in the pp-wave geometry and describe how both the chiral multiplets and semi-conserved multiplets fall into N=8 supermultiplets.

hep-th↗

arXiv2002

Domain Wall from Gauged d=4, N=8 Supergravity: Part I

By studying already known extrema of non-semi-simple Inonu-Wigner contraction CSO(p, q)^{+} and non-compact SO(p, q)^{+}(p+q=8) gauged N=8 supergravity in 4-dimensions developed by Hull sometime ago, one expects there exists nontrivial flow in the 3-dimensional boundary field theory. We find that these gaugings provide first-order domain-wall solutions from direct extremization of energy-density. We also consider the most general CSO(p, q, r)^{+} with p+q+r=8 gauging of N=8 supergravity by two successive SL(8,R) transformations of the de Wit-Nicolai theory, that is, compact SO(8) gauged supergravity. The theory found earlier has local SU(8)x CSO(p, q, r)^{+} gauge symmetry as well as local N=8 supersymmetry. The gauge group CSO(p, q, r)^{+} is spontaneously reduced to its maximal compact subgroup SO(p)^{+} x SO(q)^{+} x U(1)^{+r(r-1)/2}. The T-tensor we obtain describes a two-parameter family of gauged N=8 supergravity from which one can construct A_1 and A_2 tensors. The effective nontrivial scalar potential can be written as the difference of positive definite terms. We examine the scalar potential for critical points at which the expectation value of the scalar field is SO(p)^{+} x SO(q)^{+} x SO(r)^{+} invariant. It turns out that there is no new extra critical point. However, we do have flow equations and domain-wall solutions for the scalar fields are the gradient flow equations of the superpotential that is one of the eigenvalues of A_1 tensor.

hep-th↗

arXiv2002

An N=1 Supersymmetric G_2-invariant Flow in M-theory

It was found that deformation of S^7 gives rise to renormalization group(RG) flow from N=8, SO(8)-invariant UV fixed point to N=1, G_2-invariant IR fixed point in four-dimensional gauged N=8 supergravity. Also BPS supersymmetric domain wall configuration interpolated between these two critical points. In this paper, we use the G_2-invariant RG flow equations for both scalar fields and domain-wall amplitude and apply them to the nonlinear metric ansatz developed by de Wit, Nicolai and Warner some time ago. We carry out the M-theory lift of the G_2-invariant RG flow through a combinatoric use of the four-dimensional RG flow equations and eleven-dimensional Einstein-Maxwell equations. The nontrivial r(that is the coordinate transverse to the domain wall)-dependence of vacuum expectation values becomes consistent with not only at the critical points but also along the supersymmetric RG flow connecting two critical points. By applying an ansatz for an eleven-dimensional three-form gauge field with varying scalars, we discover an exact solution to the eleven-dimensional Einstein-Maxwell equations corresponding to the M-theory lift of the G_2-invariant RG flow.

hep-th↗

arXiv2001

Orientifold in Conifold and Quantum Deformation

We describe orientifold operation defining O3 plane in the conifold background by deriving it from that of O4 plane in the Type IIA brane construction by T-duality. We find that both $O3^+$ and $O3^-$ are at the tip of the cone so that there is no net untwisted RR charge. RG analysis shows that we need two `fractional' branes for the conformal invariance in orientifolded conifold. We argue that the gravity solution is the same as Klebanov and Tsyetlin since SUGRA cannot distinguish the orientifolds and D branes in this case. We describe the duality cascade as well as the quantum deformation of the moduli space of the field theory in the presence of the orientifold. The finitely resolved conifold does not allow the orientifold, while deformed conifold leaves us an unresolved issue on supersymmetry.

hep-th↗