I. Y. Park
In arXiv:0801.0218 [hep-th] it was conjectured that quantum effects of open strings moving on D-branes generate the D-brane geometry through a counter-vertex operator. The conjecture has been checked at one-loop in arXiv:0806.3330 [hep-th]. Here we discuss the two-loop extension.
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We study vertex operators for super Yang-Mills and multi D-branes in covariant form using Green-Schwarz formalism. We introduce the contact terms naturally and prove space-time supersymmetry and gauge invariance. The nonlinear realization of broken supersymmetry in the presence of D-branes is also discussed. The shift of fermionic coordinate δ^{(-)}Ψ=ηbecomes exact symmetry of D-brane in the static gauge, where $η$ is a constant spinor in U(1) direction.
We study baryons in SU(N) gauge theories, according to the gauge/string correspondence based on IIB string theory. The D5 brane, in which $N$ fundamental strings are dissolved as a color singlet, is introduced as the baryon vertex, and its configurations are studied. We find point- and split-type of vertex. In the latter case, two cusps appears and they are connected by a flux composed of dissolved fundamental strings with a definite tension. In both cases, $N$ fundamental quarks are attached on the cusp(s) of the vertex to cancel the surface term. In the confining phase, we find that the quar…
In this paper we explicitly work out the precise relationship between Ext groups and massless modes of D-branes wrapped on complex submanifolds of Calabi-Yau manifolds. Specifically, we explicitly compute the boundary vertex operators for massless Ramond sector states, in open string B models describing Calabi-Yau manifolds at large radius, directly in BCFT using standard methods. Naively these vertex operators are in one-to-one correspondence with certain sheaf cohomology groups (as is typical for such vertex operator calculations), which are related to the desired Ext groups via spectral seq…
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.
Starting with a new bosonization scheme for the βγCFT of the super-conformal ghosts, vertex operators are constructed for massless open string states in the intersecting D-brane world. These vertex operators satisfy all requirements for a consistent RNS formulation of superstring theories, so GSO projections can be properly taken.
We propose a full-fledged open string framework that seems suited to study the black hole information paradox. We set up a configuration to compute the scattering amplitude of a IIB open string around a D5-brane. The D5-brane is situated at the origin of a transverse D3-brane. A string perturbation theory is employed where the geometry of the D5-brane is treated as a potential. We reason that the setup is capable of reconciling the unitary evolution of states and information loss that is measured by an observer on the D3 brane. With the configurations of these kinds, the information loss is an…
We propose refined topological vertex formalism for 5-brane systems with ON-planes by introducing a new vertex associated with reflection over an ON-plane, which gives rise to new vertex and edge factors. We test our proposal against various 5d $\mathcal{N}=1$ gauge theories which can be realized as 5-brane webs with ON-planes, which include $D$-type quiver theories. In particular, we compute the refined partition functions for 6d E-string theory on a circle as well as 5d SU(3) theory at the Chern-Simons level 9, which can be realized as 5-brane webs with two ON-planes. Our results completely …
We consider Type IIB 5-brane web diagrams for a 5D $Sp(N)$ gauge theory with an antisymmetric hypermultiplet and $N_f$ fundamental hypermultiplets. The corresponding 5-branes can be obtained by Higgsing a 5-brane web for quiver gauge theory. We use the refined topological vertex formalism to compute Nekrasov partition functions of 5D $Sp(2)$ theories with one antisymmetric hypermultiplet and flavors. Our results agree with the known results obtained from the ADHM method. We also discuss a particular tuning of Kähler parameters associated with this Higgsing.
In a direct open string approach we analyze scattering of massless states on a stack of D3-branes. First we construct vertex operators on the D-branes. The 4+6 splitting for the fermionic part is made possible by inserting appropriately defined projection operators. With the vertex operators constructed we compute various tree amplitudes. The results are then compared with the corresponding field theory computations of the $\N=4$ SYM with $\a'$-corrections: agreements are found. We comment on applications to AdS/CFT.
We propose a concrete form of a vertex function, which we call O-vertex, for the intersection between an O5-plane and a 5-brane in the topological vertex formalism, as an extension of the work of arXiv:1709.01928. Using the O-vertex it is possible to compute the Nekrasov partition functions of 5d theories realized on any 5-brane web diagrams with O5-planes. We apply our proposal to 5-brane webs with an O5-plane and compute the partition functions of pure SO($N$) gauge theories and the pure $G_2$ gauge theory. The obtained results agree with the results known in the literature. We also compute …
We study the effect of adding lower dimensional brane charges to the 't Hooft monopole, di-baryon and baryon vertex configurations in AdS_4 x CP^3. We show that these configurations capture the background fluxes in a way that depends on the induced charges, requiring additional fundamental strings to cancel the worldvolume tadpoles. The dynamics reveal that the charges must lie inside some interval, a situation familiar from the baryon vertex in AdS_5 x S^5 with charges. For the baryon vertex and the di-baryon the number of fundamental strings must also lie inside an allowed interval. Some ide…
We propose a DBI vertex brane + $N_c$ fundamental strings configuration for a probe baryon in the finite-temperature thermal gauge field via AdS/CFT correspondence. In particular, we investigate properties of this configuration in QCD_4 and warped AdS_6\times S^4. We find that, in D4-D8 system, a holographic probe baryon can be described as N_c fundamental strings connecting through a vertex D4 brane wrapped on S^4. In QCD_4 background, a closed vertex can exist in confined phase and can not exist in deconfined phase. In the low temperature region, screening effect still exist in confined phas…
We argue the connection of Nekrasov's partition function in the Ωbackground and the moduli space of D-branes, suggested by the idea of geometric engineering and Gopakumar-Vafa invariants. In the instanton expansion of N=2 SU(2) Yang-Mills theory the Nakrasov's partition function with equivariant parameters ε_1, ε_2 of toric action on C^2 factorizes correctly as the character of SU(2)_L \times SU(2)_R spin representation. We show that up to two instantons the spin contents are consistent with the Lefschetz action on the moduli space of D2-branes on (local) F_0. We also present an attempt at con…
We study the effect of adding lower dimensional brane charges to the 't Hooft monopole, di-baryon and baryon vertex configurations in $AdS_4 \times \mathbb{P}^3$. We show that these configurations capture the background fluxes in a way that depends on the induced charges, and therefore, require additional fundamental strings in order to cancel the worldvolume tadpoles. The study of the dynamics reveals that the charges must lie inside some interval in order to find well defined configurations, a situation familiar from the baryon vertex in $AdS_5 \times S^5$ with charges. For the baryon vertex…
Witten couples the open topological B-model to a holomorphic vector bundle by adding to the boundary of the worldsheet a Wilson loop for an integrable connection on the bundle. Using the descent procedure for boundary vertex operators in this context, I generalize this construction to write a worldsheet coupling for a graded vector bundle with an integrable superconnection. I then compute the open string vertex operators between two such boundaries. A theorem of J. Block gives that this is equivalent to coupling the B-model to an arbitrary object in the derived category.
We analyze one loop scattering amplitudes of the massless states on a stack of D3-branes. We use the vertex operators that have been obtained in the direct open string analysis developed in arXiv:0708.3452. The method does not have the obstacle of the D9 computation which is associated with the appearance of an $\e$-tensor. The divergence structure is not the same as the D9 brane case. What makes the analysis deviate from the D9 brane case is that the momenta of the states have non-zero components only along the brane directions. We ponder on the possibility that the one-loop divergence may be…
We provide a direct world-sheet derivation of the couplings of NS-NS and R-R fluxes to various types of D-branes (including instantonic ones) by evaluating disk amplitudes among two open string vertex operators at a generic brane intersection and one closed string vertex representing the background fluxes. This world-sheet approach is in full agreement with the derivation of the flux couplings in the brane effective actions based on supergravity methods, but it is applicable also to more general brane configurations involving fields with twisted boundary conditions. As an application, we consi…
The baryon vertex of IIB superstring theory on $AdS_{5}\times \mathbb{R}P^{5}$, for the case of orthogonal groups, is studied. The energy of the three brane decayed from an original five brane is calculated explicitly. The radius of this decayed three brane, for a BPS configuration, is also given and interpreted.
Method for computing scattering amplitudes of open strings with Dirichlet boundary on one end and Neumann boundary condition on the other is described. Vertex operator for these states are constructed using twist fields which have been studied previously in the context of Ashkin-Teller model and strings on orbifolds. Using these vertex operators, we compute the three- and four-point scattering amplitudes for (5,9) strings on 5-branes and 9-branes. In the low energy limit, these amplitudes are found to be in exact agreement with the field theory amplitudes for supersymmetric Yang-Mills coupled …
Topological Vertex for Symmetric matter
针对含对称张量超多重态的5维$\mathcal{N}=1$ SU($N$)规范理论，基于O7$^+$-平面膜构造引入$\mathbb{Z}_2$-顶点与FD-顶点，推广拓扑顶点形式体系，建立配分函数计算方法并给出杨图求和表达式。
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 $D$-insta…
The cubic interaction vertex and the dynamical supercharges are constructed for open strings ending on D7-branes, in light-cone superstring field theory in PP-wave background. In this context, we write down the symmetry generators in terms of the relevant group structure: SU(2) x SU(2) x SO(2) x SO(2), originating from the eight transverse directions in the PP-wave background and use the expressions to explicitly construct the vertex at the level of stringy zero modes. The results are further generalized to include all the stringy excitations as well.
Given a Calabi-Yau manifold and considering the $B$-branes on it as objects in the derived category of coherent sheaves, we identify the vertex operators for strings between two branes with elements of the cohomology groups of Ext sheaves. We define the correlation functions for these general vertex operators. Strings stretching between two coherent sheaves are studied as homological extensions of the corresponding branes. In this context, we relate strings between different pairs of branes when there are maps between these branes. We also interpret some strings with ghost number $k$ as obstru…
We study the open refined topological string amplitudes using the refined topological vertex. We determine the refinement of holonomies necessary to describe the boundary conditions of open amplitudes (which in particular satisfy the required integrality properties). We also derive the refined holonomies using the refined Chern-Simons theory.
Brane-like vertex operators play an important role in a worldsheet formulation of D-branes and M-theory. In this paper we derive the DBI D-brane action from NSR closed string sigma-model with brane-like states. We also show that these operators carry RR charges and define D-brane wavefunctions in a second quantized formalism.
We propose a new approach for coupling the type II superstring to the Ramond-Ramond background of D-branes in the RNS formalism, alternative to introducing RR vertex operators. It is based on the mixing between Ramond-Ramond p-form excitations in the closed string spectrum and transversally polarized excitations in the open string spectrum.
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 cub…
We show that Calabi-Yau crystals generate certain Chern-Simons knot invariants, with Lagrangian brane insertions generating the unknot and Hopf link invariants. Further, we make the connection of the crystal brane amplitudes to the topological vertex formulation explicit and show that the crystal naturally resums the corresponding topological vertex amplitudes. We also discuss the conifold and double wall crystal model in this context. The results suggest that the free energy associated to the crystal brane amplitudes can be simply expressed as a target space Gopakumar-Vafa expansion.
Boundary states for D-branes are constructed using the light cone gauge. The D-brane breaks half the spacetime supersymmetry giving rise to fermionic zero modes living on the brane. The nonlinear realization of the broken supersymmetry on the open string degrees of freedom is analysed and the influence of boundary terms coming from closed string vertex operators is discussed.
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 t…
We develop an operator formalism to compute scattering amplitudes of arbitrary bosonic string states in the background of many D-branes. Specifically, we construct a suitable boundary state which we use to saturate the multi-Reggeon vertex in order to obtain the generator of multi-membrane scattering amplitudes. We explicitly show that the amplitudes with $h$ parallel D-branes are similar to amplitudes with $h-1$ open string loops.
We construct the cubic interaction vertex and dynamically generated supercharges in light-cone superstring field theory for a large class half-supersymmetric D-branes in the plane-wave background. We show that these satisfy the plane-wave superalgebra at first order in string coupling. The cubic interaction vertex and dynamical supercharges presented here are given explicitly in terms of oscilators and can be used to compute three-point functions of open strings with endpoints on half-supersymmetric D-branes.
We study the Regge trajectories of holographic mesons and baryons by considering rotating strings and D5 brane, which is introduced as the baryon vertex. Our model is based on the type IIB superstring theory with the background of asymptotic $AdS_5\times S^5$. This background is dual to a confining supersymmetric Yang-Mills theory (SYM) with gauge condensate, $<F^2>$, which determines the tension of the linear potential between the quark and anti-quark. Then the slope of the meson trajectory ($α'_{M}$) is given by this condensate as $α'_{M}=1/\sqrt{π<F^2>}$ at large spin $J$. This relation is …
A large class of D-branes in Calabi-Yau spaces can be constructed at the Gepner points using the techniques of boundary conformal field theory. In this note we develop methods that allow to compute open string amplitudes for such D-branes. In particular, we present explicit formulas for the products of open string vertex operators of untwisted A-type branes. As an application we show that the boundary theories of the quintic associated with the special Lagrangian submanifolds Im ω_i z_i = 0 where ω_i^5=1 possess no continuous moduli.
We discuss the NSR formulation of the superstring action on AdS_5 X S^5 proposed recently by Kallosh and Tseytlin in the Green-Schwarz formalism.We show that the stress-energy tensor corresponding to the NSR action for AdS superstring contains the branelike terms, corresponding to exotic massless vertex operators (refered to as the branelike vertices). The corresponding sigma-model action has the manifest SO(1,3) X SO(6) invariance of superstring theory on AdS_5 X S^5. We argue that adding the branelike terms is equivalent to curving the space-time to obtain the AdS_5 X S^5 background. We comm…
The Wess-Zumino coupling on D-branes in string theory is known to receive higher derivative corrections which couple the Ramond-Ramond potential to terms involving the square of the spacetime curvature tensor. Consistency with T-duality implies that the branes should also have four-derivative couplings that involve the NS-NS B-field. We use T-duality to predict some of these couplings. We then confirm these results with string worldsheet computations by evaluating disc amplitudes with insertions of one R-R and two NS-NS vertex operators.
A conjecture for computing all genus topological closed string amplitudes on toric local Calabi-Yau threefolds, by interpreting the associated 5-brane web as a Feynman diagram, is given. A propagator and a three point vertex is defined which allows us to write down the amplitude associated with 5-brane web. We verify the conjecture that this amplitude is equal to the closed string partition function by computing integer invariants for resolved conifold and certain curves of low degree in local del Pezzo surfaces, local Hirzebruch surfaces and their various blowups.
We study conformal field theory correlation functions relevant for string diagrams with open strings that stretch between several parallel branes of different dimensions. In the framework of conformal field theory, they involve boundary condition changing twist fields which intertwine between Neumann and Dirichlet conditions. A Knizhnik-Zamolodchikov-like differential equation for correlators of such boundary twist fields and ordinary string vertex operators is derived, and explicit integral formulas for its solutions are provided.
In the mapping from four-dimensional gauge theories to string theory in $AdS$ space, many features of gauge theory can be described by branes wrapped in different ways on $§^5$, $\RP^5$, or subspaces thereof. These include a baryon vertex coupling N external charges in the fundamental representation of SU(N), a bound state of $k$ gluons in SO(2k) gauge theory, strings coupled to external charges in the spinor representation of the gauge group, and domain walls across which the low energy gauge group changes.
We propose a string-theoretic ansatz describing the dynamics of SU(N) Yang-Mills theories in the limit of large N in D=4. The construction uses in a crucial way open-string vertex operators that describe non-perturbative brane dynamics. According to our proposal, various gauge theories are described by string theories with the same action, but with different measures in the functional integral. The choice of measure defines the gauge group, as well as the effective space-time dimension of the resulting gauge theory.
We discuss two inequivalent ways for describing magnetized D-branes wrapped N times on a torus T^2. The first one is based on a non-abelian gauge bundle U(N), while the second one is obtained by means of a Narain T-duality transformation acting on a theory with non-magnetized branes. We construct in both descriptions the boundary state and the open string vertices and show that they give rise to different string amplitudes. In particular, the description based on the gauge bundle has open string vertex operators with momentum dependent Chan-Paton factors.
We study M theory on $AdS_7 \times \RP^4$ corresponding to 6 dimensional SO(2N) $(0, 2)$ superconformal field theory on a circle which becomes 5 dimensional super Yang-Mills theory at low energies. For SU(N) (0,2) theory, a wrapped D4 brane on $§^4$ which is connected to a D4 brane on the boundary of $AdS_7$ by N fundamental strings can be interpreted as baryon vertex. For SO(2N) (0,2) theory, by using the property of homology of $\RP^4$, we classify various wrapping branes. Then we consider particles, strings, twobranes, domain walls and the baryon vertex in Type IIA string theory.
We consider interactions of a NS open string with first important states of a NS closed string, i.e., a closed-string tachyon and a graviton, where both ends of the NS open string are attached on a D-brane, and a constant background B field is lying along directions parallel to the D-brane world volume. Contrary to general expectations, there are no constraints on these vertex operators coming from the B field. However, we point out that these vertex operators have singularities at both ends of the NS open string when external momenta take some values. These kinds of singularities essentially …
We propose a generalization of the topological vertex, which we call the "non-commutative topological vertex". This gives open BPS invariants for a toric Calabi-Yau manifold without compact 4-cycles, where we have D0/D2/D6-branes wrapping holomorphic 0/2/6-cycles, as well as D2-branes wrapping disks whose boundaries are on D4-branes wrapping non-compact Lagrangian 3-cycles. The vertex is defined combinatorially using the crystal melting model proposed recently, and depends on the value of closed string moduli at infinity. The vertex in one special chamber gives the same answer as that computed…
We study D-branes that preserve a diagonal SL(2) affine Lie algebra in string theory on AdS_3. We find three classes of solutions, corresponding to the following representations of SL(2): (1) degenerate, finite dimensional representations with half integer spin, (2) principal continuous series, (3) principal discrete series. We solve the bootstrap equations for the vacuum wave functions and discuss the corresponding open string spectrum. We argue that from the point of view of the AdS/CFT correspondence, the above D-branes introduce boundaries with conformal boundary conditions into the two di…
We write the vertex operators of massless NS-NS and RR states of Type II superstring theory in the presence of Orientifold p-planes. They include the usual vertex operators of Type II theory and their images. We then calculate the two-point functions of these vertex operators at the projective plane PR_2 level. We show that the result can be written in the Veneziano-type formulae, with the same kinematic factor that appears in the D_p-branes amplitudes. While the scattering amplitudes with the usual vertex operators are not gauge invariant, the above amplitudes are invariant. From the amplitud…
One-loop scattering on a stack of D3 branes was considered in arXiv:0801.0218 [hep-th]. Divergence was found and its cancelation mechanism was proposed, wherein it was conjectured that the D-brane geometry be introduced in the form of counter vertex operators. Here we verify the conjecture at the first few leading orders in an expansion method that we call large-$r_0$ expansion. We comment on the relation with the Fischler-Susskind mechanism and discuss the implications of our result for AdS/CFT.
In our continued efforts of matching full string computations with the corresponding effective field theory computations, we evaluate string theory correlators in closed forms. In particular, we consider a correlator between three SYM vertex operators and one Ramond-Ramond $C$-field vertex operator: $<V_{C}V_ϕ V_AV_A>$. We show that the infinite number of massless poles of this amplitude can be reproduced by the Born-Infeld action, the Wess-Zumino terms, and their higher derivative corrections. More specifically we find, up to an on-shell ambiguity, two scalar field and two gauge field couplin…
We propose a class of toric Lagrangian A-branes on the resolved conifold that is suitable to describe torus knots on S^3. The key role is played by the SL(2,Z) transformation, which generates a general torus knot from the unknot. Applying the topological vertex to the proposed A-branes, we rederive the colored HOMFLY polynomials for torus knots, in agreement with the Rosso and Jones formula. We show that our A-model construction is mirror symmetric to the B-model analysis of Brini, Eynard and Marino. Comparing to the recent proposal by Aganagic and Vafa for knots on S^3, we demonstrate that th…
We study branes and open strings in a large class of orbifolds of a curved background using microscopic techniques of boundary conformal field theory. In particular, we obtain factorizing operator product expansions of open string vertex operators for such branes. Applications include branes in Z2 orbifolds of the SU(2) WZW model and in the D-series of unitary minimal models considered previously by Runkel.
We establish a direct map between refined topological vertex and sl(N) homological invariants of the of Hopf link, which include Khovanov-Rozansky homology as a special case. This relation provides an exact answer for homological invariants of the of Hopf link, whose components are colored by arbitrary representations of sl(N). At present, the mathematical formulation of such homological invariants is available only for the fundamental representation (the Khovanov-Rozansky theory) and the relation with the refined topological vertex should be useful for categorifying quantum group invariants a…
Using the pure spinor formalism, a particular superstring scattering amplitude involving one closed string and $N$ open string vertex operators in $\mathrm{AdS}{}_5 \times \mathrm{S}^5$ is studied. It is shown that the tree-level amplitude containing one supergravity state and $N$ super-Yang-Mills states located on D3-branes near the AdS${}_5$ boundary can be expressed as a $d=4$ ${\cal N}=4$ harmonic superspace integral in terms of the supergravity and super-Yang-Mills superfields.
A vertex algebra is an algebraic counterpart of a two-dimensional conformal field theory. We give a new definition of a vertex algebra which includes chiral algebras as a special case, but allows for fields which are neither meromorphic nor anti-meromorphic. To any complex torus equipped with a flat Kahler metric and a closed 2-form we associate an N=2 superconformal vertex algebra (N=2 SCVA) in the sense of our definition. We find a criterion for two different tori to produce isomorphic N=2 SCVA's. We show that for algebraic tori isomorphism of N=2 SCVA's implies the equivalence of the derive…
Tropical Branes
本文提出热带膜概念，通过正则量子化开弦解给出热带拓扑sigma模型的非相对论膜对应物，并提供初步世界面描述，为后续膜量子化研究奠定基础。
The eikonal operator was originally introduced to describe the effect of tidal excitations on higher-genus elastic string amplitudes at high energy. In this paper we provide a precise interpretation for this operator through the explicit tree-level calculation of generic inelastic transitions between closed strings as they scatter off a stack of parallel Dp-branes. We perform this analysis both in the light-cone gauge, using the Green-Schwarz vertex, and in the covariant formalism, using the Reggeon vertex operator. We also present a detailed discussion of the high energy behaviour of the cova…
String-brane interactions provide an ideal framework to study the dynamics of the massive states of the string spectrum in a non-trivial background. We present here an analysis of tree-level amplitudes for processes in which an NS-NS string state from the leading Regge trajectory scatters from a D-brane into another state from the leading Regge trajectory, in general of a different mass, at high energies and small scattering angles. This is done by using world-sheet OPE methods and effective vertex operators. We find that this class of processes has a universal dependence on the energy of the …
We introduce a new type IIB 5-brane description for the E-string theory which is the world-volume theory on the M5-brane probing the end of the world M9-brane. The E-string in the new realization is depicted as spiral 5-branes web equipped with the cyclic structure which is key to uplifting to six dimensions. Utilizing the topological vertex to the 5-brane web configuration enables us to write down a combinatorial formula for the generating function of the E-string elliptic genera, namely the full partition function of topological strings on the local 1/2 K3 surface.
We study both the direct and the double dimensional reduction of space-like branes of M-theory and point out some peculiarities in the process unlike their time-like counterpart. In particular, we show how starting from SM2 and SM5-brane solutions we can obtain SD2 and SNS5-brane as well as SNS1 and SD4-brane solutions of string theory by direct and double dimensional reductions respectively. In the former case we need to use delocalized SM-brane solutions, whereas in the latter case we need to use anisotropic SM-brane solutions in the directions which are compactified.
We study aspects of the vertex operator algebra (VOA) corresponding to Argyres-Douglas (AD) theories engineered using the 6d N=(2, 0) theory of type $J$ on a punctured sphere. We denote the AD theories as $(J^b[k],Y)$, where $J^b[k]$ and $Y$ represent an irregular and a regular singularity respectively. We restrict to the `minimal' case where $J^b[k]$ has no associated mass parameters, and the theory does not admit any exactly marginal deformations. The VOA corresponding to the AD theory is conjectured to be the W-algebra $\mathcal{W}^{k_{2d}}(J,Y)$, where $k_{2d}=-h+ \frac{b}{b+k}$ with $h$ b…
In this paper we continue studying the decay of unstable FZZT branes initiated in [1],[2]. The mass of tachyonic mode in this model can be chosen arbitrarily small and we use it as a perturbative parameter. In [2] a time-dependent boundary conformal field theory (BCFT) describing the decay process was studied and it was shown that in a certain sense this BCFT interpolates between two stationary BCFT's corresponding to the UV and IR fixed points of the associated RG flow. In the present work we find in the leading order vertex operators of the time-dependent BCFT. We identify the "in" and "out"…
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