arXiv subjects

Piljin Yi

Publications and source records attributed to Piljin Yi.

At least 55 records · Page 3Linked to original sources

arXiv2006

Magnetic Monopole Dynamics, Supersymmetry, and Duality

We review the properties of BPS, or supersymmetric, magnetic monopoles, with an emphasis on their low-energy dynamics and their classical and quantum bound states. After an overview of magnetic monopoles, we discuss the BPS limit and its relation to supersymmetry. We then discuss the properties and construction of multimonopole solutions with a single nontrivial Higgs field. The low-energy dynamics of these monopoles is most easily understood in terms of the moduli space and its metric. We describe in detail several known examples of these. This is then extended to cases where the unbroken gauge symmetry include a non-Abelian factor. We next turn to the generic supersymmetric Yang-Mills (SYM) case, in which several adjoint Higgs fields are present. Working first at the classical level, we describe the effects of these additional scalar fields on the monopole dynamics, and then include the contribution of the fermionic zero modes to the low-energy dynamics. The resulting low-energy effective theory is itself supersymmetric. We discuss the quantization of this theory and its quantum BPS states, which are typically composed of several loosely bound compact dyonic cores. We close with a discussion of the D-brane realization of ${\cal N}=4$ SYM monopoles and dyons and explain the ADHMN construction of monopoles from the D-brane point of view.

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arXiv2006

A Heterotic Flux Background and Calibrated Five-Branes

We consider, in flux compactification of heterotic string theory, spacetime-filling five-branes. Stabilizing the fivebrane involves minimizing the combined energy density of the tension and a Coulomb potential associated with an internal 2-dimensional wrapping. After reviewing the generalized calibration under such circumstances, we consider a particular internal manifold based on a $T^2$ bundle over a conformally rescaled $K3$. Here, we find two distinct types of wrapping. In one class, the fivebrane wraps the fibre $T^2$ which belongs to a cyclic homotopy group. The winding number is not extensive, yet it maps to D3-brane number under a U-duality map to type IIB side. We justify this by comparing properties of the two sides in detail. Fivebranes may also wrap a topological 2-cycle of K3, by saturating a standard calibration requirement with respect to a closed Kähler 2-form $J_{K3}$ of $K3$. We close with detailed discussion on F-theory dual of these objects and related issues.

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arXiv2006

Comments on Heterotic Flux Compactifications

In heterotic flux compactification with supersymmetry, three different connections with torsion appear naturally, all in the form $ω+a H$. Supersymmetry condition carries $a=-1$, the Dirac operator has $a=-1/3$, and higher order term in the effective action involves $a=1$. With a view toward the gauge sector, we explore the geometry with such torsions. After reviewing the supersymmetry constraints and finding a relation between the scalar curvature and the flux, we derive the squared form of the zero mode equations for gauge fermions. With $\d H=0$, the operator has a positive potential term, and the mass of the unbroken gauge sector appears formally positive definite. However, this apparent contradiction is avoided by a no-go theorem that the compactification with $H\neq 0$ and $\d H=0$ is necessarily singular, and the formal positivity is invalid. With $\d H\neq 0$, smooth compactification becomes possible. We show that, at least near smooth supersymmetric solution, the size of $H^2$ should be comparable to that of $\d H$ and the consistent truncation of action has to keep $α'R^2$ term. A warp factor equation of motion is rewritten with $α' R^2$ contribution included precisely, and some limits are considered.

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arXiv2005

Reheating the Universe after String Theory Inflation

In String theory realizations of inflation, the end point of inflation is often brane-anti brane annihilation. We consider the processes of reheating of the Standard Model universe after brane inflation. We identify the channels of inflaton energy decay, cascading from tachyon annihilation through massive closed string loops, KK modes, and brane displacement moduli to the lighter standard model particles. Cosmological data constrains scenarios by putting stringent limits on the fraction of reheating energy deposited in gravitons and nonstandard sector massive relics. We estimate the energy deposited into various light degrees of freedom in the open and closed string sectors, the timing of reheating, and the reheating temperature. Production of gravitons is significantly suppressed in warped inflation. However, we predict a residual gravitational radiation background at the level $Ω_{GW} \sim 10^{-8}$ of the present cosmological energy density. We also extend our analysis to multiple throat scenarios. A viable reheating would be possible in a single throat or in a certain subclass of multiple throat scenarios of the KKLMMT type inflation model, but overproduction of massive KK modes poses a serious problem. The problem is quite severe if some inner manifold comes with approximate isometries (angular KK modes) or if there exists a throat of modest length other than the standard model throat, possibly associated with some hidden sector (low-lying KK modes).

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arXiv2005

Winding Strings and Decay of D-Branes with Flux

We study the boundary state associated with the decay of an unstable D-brane with uniform electric field, 1>e>0 in the string units. Compactifying the D-brane along the direction of the electric field, we find that the decay process is dominated by production of closed strings with some winding numbers; closed strings produced are such that the winding mode carries precisely the fraction $e$ of the individual string energy. This supports the conjecture that the final state at tree level is composed of winding strings with heavy oscillations turned on. As a corollary, we argue that the closed strings disperse into spacetime at a much slower rate than the case without electric field.

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arXiv2004

The N=1* Theories on R^{1+2} X S^1 with Twisted Boundary Conditions

We explore the N=1* theories compactified on a circle with twisted boundary conditions. The gauge algebra of these theories are the so-called twisted affine Lie algebra. We propose the exact superpotentials by guessing the sum of all monopole-instanton contributions and also by requiring SL(2,Z) modular properties. The latter is inherited from the N=4 theory, which will be justified in the M theory setting. Interestingly all twisted theories possess full SL(2,Z) invariance, even though none of them are simply-laced. We further notice that these superpotentials are associated with certain integrable models widely known as elliptic Calogero-Moser models. Finally, we argue that the glueball superpotential must be independent of the compactification radius, and thus of the twisting, and confirm this by expanding it in terms of glueball superfield in weak coupling expansion.

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arXiv2004

Open/Closed Duality, Unstable D-Branes, and Coarse-Grained Closed Strings

At the final stage of unstable D-brane decay in the effective field theory approach, all energy and momentum of the initial state are taken up by two types of fluids, known as string fluid and tachyon matter. In this note, we compare motion of this fluid system to that of macroscopic collection of stretched closed strings and find a precise match at classical level. The string fluid reflects low frequency undulation of the stretched strings while the tachyon matter encodes the average effect of high frequency oscillations turned on those strings. In particular, the combined fluid system has been known to have a reduced speed of light, depending on the composition, and we show that this property is exactly reproduced in classical motion on the closed string side. Finally we illustrate how the tachyon matter may be viewed as an effective degrees of freedom carrying high frequency energy-momentum of Nambu-Goto strings by coarse-graining the dynamics of the latter.

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arXiv2004

A Holographic View on Matrix Model of Black Hole

We investigate a deformed matrix model proposed by Kazakov et.al. in relation to Witten's two-dimensional black hole. The existing conjectures assert the equivalence of the two by mapping each to a deformed c=1 theory called the sine-Liouville theory. We point out that the matrix theory in question may be naturally interpreted as a gauged quantum mechanics deformed by insertion of an exponentiated Wilson loop operator, which gives us more direct and holographic map between the two sides. The matrix model in the usual scaling limit must correspond to the bosonic SL(2,R)/U(1) theory in genus expansion but exact in α'. We successfully test this by computing the Wilson loop expectation value and comparing it against the bulk computation. For the latter, we employ the α'-exact geometry proposed by Dijkgraaf, Verlinde, and Verlinde, which was further advocated by Tseytlin. We close with comments on open problems.

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arXiv2003

Tachyon Tube and Supertube

We search for tubular solutions in unstable D3-brane. With critical electric field E=1, solutions representing supertubes, which are supersymmetric bound states of fundamental strings, D0-branes, and a cylindrical D2-brane, are found and shown to exhibit BPS-like property. We also point out that boosting such a {\it tachyon tube} solution generates string flux winding around the tube, resulting in helical electric fluxes on the D2-brane. We also discuss issues related to fundamental string, absence of magnetic monopole, and finally more tachyon tubes with noncritical electric field.

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arXiv2003

String Fluid, Tachyon Matter, and Domain Walls

We study classical dynamics of an open string tachyon $T$ of unstable D$p$-brane coupled to the gauge field $A_μ$. In the vacuum with vanishing potential, V=0, two fluid-like degrees of freedom, string fluid and tachyon matter, survive the tachyon condensation. We offer general analysis of the associated Hamiltonian dynamics in arbitrary background. The canonical field equations are organized into two sets, fluid equations of motion augmented by an integrability condition. We show that a large class of motionless and degenerate family of classical solutions exist and represent arbitrary transverse distribution of tachyon matter and flux lines. We further test their stability by perturbing the fluid equation up to the second order. Second half of this note considers possibility of $V \neq 0$ in the dynamics. We incorporate $V$ in the Hamiltonian equation of motion and consider interaction between domain walls and string fluid. During initial phase of tachyon condensation, topological defect at T=0 is shown to attract nearby and parallel flux lines. The final state is fundamental strings absorbed and spread in some singular D$(p-1)$ brane soliton. When string fluid is transverse to the domain wall, the latter is known to turn into a smooth solution. We point out that a minimal solution of this sort exists and saturates a BPS energy bound of fundamental string ending on a D$(p-1)$ brane.

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arXiv2003

Instantons of M(atrix) Theory in PP-Wave Background

M(atrix) theory in PP-wave background possesses a discrete set of classical vacua, all of which preserves 16 supersymmetry and interpretable as collection of giant gravitons. We find Euclidean instanton solutions that interpolate between them, and analyze their properties. Supersymmetry prevents direct mixing between different vacua but still allows effect of instanton to show up in higher order effective interactions, such as analog of v^4 interaction of flat space effective theory. An explicit construction of zero modes is performed, and Goldstone zero modes, bosonic and fermionic, are identified. We further generalize this to massive M(atrix) theory that includes fundamental hypermultiplets, corresponding to insertion of longitudinal fivebranes in the background. After a brief comparison to their counterpart in AdS\times S, we close with a summary.

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arXiv2002

Tachyon Condensates, Carrollian Contraction of Lorentz Group, and Fundamental Strings

We study the rolling tachyon condensate in the presence of a gauge field. The generic vacuum admits both a rolling tachyon, \dot{T}, and a uniform electric field, \vec{E}, which together affect the effective metric governing the fluctuations of open string modes. If one suppresses the gauge field altogether, the light-cone collapses completely. This is the Carrollian limit, with vanishing speed of light and no possible propagation of signals. In the presence of a gauge field, however, the lightcone is squeezed to the shape of a fan, allowing propagation of signals along the direction of \pm \vec{E} at speed |E|=<1. This shows that there are perturbative degrees of freedom propagating along electric flux lines. Such causal behavior appears to be a very general feature of tachyon effective Lagrangian with runway potentials. We speculate on how this may be connected to appearance of fundamental strings.

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arXiv2002

Deformed Matrix Theories with N=8 and Fivebranes in the PP Wave Background

M(atrix) theory is known to be mass-deformed in the pp-wave background and still retains all 16 dynamical supersymmetries. We consider generalization of such deformations on super Yang-Mills quantum mechanics (SYQM) with less supersymmetry. In particular this includes N=8 U(N) SYQM with a single adjoint and any number of fundamental hypermultiplets, which is a pp-wave deformation of DLCQ matrix theory of fivebranes. With k >= 1 fivebranes, we show that a rich vacuum structure exists, with many continuous family of solutions that preserve all dynamical supersymmetries. The vacuum moduli space contains copies of CP^{k-1} of various sizes.

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arXiv2001

D-Brane Probe and Closed String Tachyons

We consider a D-brane probe in unstable string background associated with flux branes. The twist in spacetime metric reponsible for the supersymmetry breaking is shown to manifest itself in mixing of open Wilson lines with the phases of some adjoint matter fields, resulting in a nonlocal and nonsupersymmetric form of Yang-Mills theory as the probe dynamics. This provides a setup where one can study fate of a large class of unstable closed string theories that include as a limit type 0 theories and various orbifolds of type II and type 0 theories. We discuss the limit of ${\bf C}/Z_n$ orbifold in some detail and speculate on couplings with closed string tachyons.

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arXiv2001

DLCQ of Fivebranes, Large N Screening, and L^2 Harmonic Forms on Calabi Manifolds

We find one explicit L^2 harmonic form for every Calabi manifold. Calabi manifolds are known to arise in low energy dynamics of solitons in Yang-Mills theories, and the L^2 harmonic form corresponds to the supersymmetric ground state. As the normalizable ground state of a single U(N) instanton, it is related to the bound state of a single D0 to multiple coincident D4's in the non-commutative setting, or equivalently a unit Kaluza-Klein mode in DLCQ of fivebrane worldvolume theory. As the ground state of nonabelian massless monopoles realized around a monopole-``anti''-monopole pair, it shows how the long range force between the pair is screened in a manner reminiscent of large N behavior of quark-anti-quark potential found in AdS/CFT correspondence.

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arXiv2001

Anomaly of (2,0) Theories

We compute gravitational and axial anomaly for D-type (2,0) theories realized on N pairs of coincident M5-branes at R^5/Z_2 orbifold fixed point. We first summarize work by Harvey, Minasian, and Moore on A-type (2,0) theories, and then extend it to include the effect of orbifold fixed point. The net anomaly inflow follows when we further take into account the consistency of T^5/Z_2 M-theory orbifold. We deduce that the world-volume anomaly is given by N{\cal J}_8 + N(2N-1)(2N-2) p_2/24 where {\cal J}_8 is the anomaly polynomial of a free tensor multiplet and p_2 is the second Pontryagin class associated with the normal bundle. This result is in accord with Intriligator's conjecture.

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arXiv2000

String Fluid from Unstable D-branes

We consider Sen's effective action for unstable D-branes, and study its classical dynamics exactly. In the true vacuum, the Hamiltonian dynamics remains well-defined despite a vanishing action, and is that of massive relativistic string fluid of freely moving electric flux lines. The energy(tension) density equals the flux density in the local co-moving frame. Furthermore, a finite dual Lagrangian exists and is related to the Nielsen-Olesen field theory of ``dual'' strings, supplemented by a crucial constraint. We conclude with discussion on the endpoint of tachyon condensation.

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arXiv2000

General Low Energy Dynamics of Supersymmetric Monopoles

We derive general low energy dynamics of monopoles and dyons in N=2 and N=4 supersymmetric Yang-Mills theories by utilising a collective coordinate expansion. The resulting new kind of supersymmetric quantum mechanics incorporates the effects of multiple Higgs fields, both in the N=2 vector multiplet and hypermultiplets, having non-vanishing expectation values.

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