On second-quantized open superstring theory

The SO(32) theory, in the limit where it is an open superstring theory, is completely specified in the light-cone gauge as a second-quantized string theory in terms of a “matrix string” model. The theory is defined by the neighborhood of a 1 + 1-dimensional fixed point theory, characterized by an Abelian gauge theory with type IB Green-Schwarz form. Non-orientability and SO(32) gauge symmetry arise naturally, and the theory effectively constructs an orientifold projection of the (weakly coupled) matrix type IIB theory (also discussed herein). The fixed point theory is a conformal field theory with boundary, defining the free string theory. Interactions involving the interior of open and closed strings are governed by a twist operator in the bulk, while string endpoints are created and destroyed by a boundary twist operator.     

Gauge couplings in four-dimensional type I string orbifolds

We compute threshold effects to gauge couplings in four-dimensional _N orientifold models of type I strings with GN = 2 and GN = 1 supersymmetry, and study their dependence on the geometric moduli. We also compute the tree-level (disk) couplings of the open sector gauge fields to the twisted closed string moduli of the orbifold in various models and study their effects and that of the one-loop threshold corrections on gauge coupling unification. We interpret the results from the (supergravity) effective theory point of view and comment on the conjectured heterotic-type I duality.     

Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity

We study some aspects of Maldacena's large-N correspondence between superconformal gauge theory on the D3-brane and maximal supergravity on AdS by introducing macroscopic strings as heavy (anti-) quark probes. The macroscopic strings are semi-infinite Type IIB strings ending on a D3-brane world-volume. We first study deformation and fluctuation of D3-branes when a macroscopic BPS string is attached. We find that both dynamics and boundary conditions agree with those for the macroscopic string in anti-de Sitter supergravity. As a by-product we clarify how Polchinski's Dirichlet and Neumann open string boundary conditions arise dynamically. We then study the non-BPS macroscopic string–anti-string pair configuration as a physical realization of a heavy quark Wilson loop. We obtain the static potential from the supergravity side and find that the potential exhibits non-analyticity of the square-root branch cut in the 't Hooft coupling parameter. We put forward non-analyticity as a prediction for large-N gauge theory in the strong 't Hooft coupling limit. By turning on the Ramond–Ramond zero-form potential, we also study the vacuum angle dependence of the static potential. We finally discuss the possible dynamical realization of the heavy N-prong string junction and of the large-N loop equation via a local electric field and string recoil thereof. Throughout comparisons of the AdS–CFT correspondence, we find that a crucial role is played by “geometric duality” between the UV and IR scales in directions perpendicular to the D3-brane and parallel ones, explaining how the AdS spacetime geometry emerges out of four-dimensional gauge theory at strong coupling. Received: 21 September 2001 / Published online: 12 November 2001     

Absorption and Hawking radiation of minimal and fixed scalars,and AdS/CFT correspondence

We present a complete derivation of absorption cross section and Hawking radiation of minimal and fixed scalars from the Strominger-Vafa model of five-dimensional black hole, starting right from the moduli space of the Dl-D5 brane system. We determine the precise coupling of this moduli space to bulk modes by using the AdS/CFT correspondence. Our methods resolve a long-standing problem regarding emission of fixed scalars. We calculate three-point correlators of operators coupling to the minimal scalars from supergravity and from SCFT, and show that both vanish. We make some observations about how the AdS/SYM correspondence implies a close relation between large-N equations of motion of d-dimensional gauge theory and supergravity equations on AdS_d+l-type backgrounds. We compare with the explicit non-local transform relating one and two dimensions in the context of c = 1 matrix model.     

Brane orbits

We complete the classification of half-supersymmetric branes in toroidally compactified IIA/IIB string theory in terms of representations of the T-duality group. As a by-product we derive a last wrapping rule for the space-filling branes. We find examples of T-duality representations of branes in lower dimensions, suggested by supergravity, of which none of the component branes follow from the reduction of any brane in ten-dimensional IIA/IIB string theory. We discuss the constraints on the charges of half-supersymmetric branes, determining the corresponding T-duality and U-duality orbits.     

Counting curves with modular forms

We consider the type IIA string compactified on the Calabi-Yau space given by a degree 12 hypersurface in the weighted projective space P⁴_(1,1,2,2,6). We express the prepotential of the low-energy effective supergravity theory in terms of a set of functions that transform covariantly under PSL(2, Z) modular transformations. These functions are then determined by monodromy properties, by singularities at the massless monopole point of the moduli space, and by S → T exchange symmetry.     

String orbifolds and quotient stacks

In this note we observe that, contrary to the usual lore, string orbifolds do not describe strings on quotient spaces, but rather seem to describe strings on objects called quotient stacks, a result that follows from simply unraveling definitions, and is further justified by a number of results. Quotient stacks are very closely related to quotient spaces; for example, when the orbifold group acts freely, the quotient space and the quotient stack are homeomorphic. We explain how sigma models on quotient stacks naturally have twisted sectors, and why a sigma model on a quotient stack would be a nonsingular CFT even when the associated quotient space is singular. We also show how to understand twist fields in this language, and outline the derivation of the orbifold Euler characteristic purely in terms of stacks. We also outline why there is a sense in which one naturally finds B≠0 on exceptional divisors of resolutions. These insights are not limited to merely understanding existing string orbifolds: we also point out how this technology enables us to understand orbifolds in M-theory, as well as how this means that string orbifolds provide the first example of an entirely new class of string compactifications. As quotient stacks are not a staple of the physics literature, we include a lengthy tutorial on quotient stacks, describing how one can perform differential geometry on stacks.     

The effective action of D‐branes in Calabi‐Yau orientifold compactifications

In this review article we study type IIB superstring compactifications in the presence of space‐time filling D‐branes while preserving 𝒩=1 supersymmetry in the effective four‐dimensional theory. This amount of unbroken supersymmetry and the requirement to fulfill the consistency conditions imposed by the space‐time filling D‐branes lead to Calabi‐Yau orientifold compactifications. For a generic Calabi‐Yau orientifold theory with space‐time filling D3‐ or D7‐branes we derive the low‐energy spectrum. In a second step we compute the effective 𝒩=1 supergravity action which describes in the low‐energy regime the massless open and closed string modes of the underlying type IIB Calabi‐Yau orientifold string theory. These 𝒩=1 supergravity theories are analyzed and in particular spontaneous supersymmetry breaking induced by non‐trivial background fluxes is studied. For D3‐brane scenarios we compute soft‐supersymmetry breaking terms resulting from bulk background fluxes whereas for D7‐brane systems we investigate the structure of D‐ and F‐terms originating from worldvolume D7‐brane background fluxes. Finally we relate the geometric structure of D7‐brane Calabi‐Yau orientifold compactifications to 𝒩=1 special geometry.     

Pseudo-supersymmetry, consistent sphere reduction and Killing spinors for the bosonic string

Certain supergravity theories admit a remarkable consistent dimensional reduction in which the internal space is a sphere. Examples include type IIB supergravity reduced on S⁵, and eleven-dimensional supergravity reduced on S⁴ or S⁷. Consistency means that any solution of the dimensionally-reduced theory lifts to give a solution in the higher dimension. Although supersymmetry seems to play a role in the consistency of these reductions, it cannot be the whole story since consistent sphere reductions of non-supersymmetric theories are also known, such as the reduction of the effective action of the bosonic string in any dimension D on either a 3-sphere or a (D−3)-sphere, retaining the gauge bosons of SO(4) or SO(D−2) respectively. We show that although there is no supersymmetry, there is nevertheless a natural Killing spinor equation for the D-dimensional bosonic string. A projection of the full integrability condition for these Killing spinors gives rise to the bosonic equations of motion (just as happens in the supergravity examples). Thus it appears that by extending the notion of supersymmetry to “pseudo-supersymmetry” in this way, one may be able to obtain a broader understanding of a relation between Killing spinors and consistent sphere reductions.     

Diagrammar and metamorphosis of coset symmetries in dimensionally reduced type IIB supergravity

Studying the reduction of type IIB supergravity from ten to three spacetime dimensions, we describe the metamorphosis of the Dynkin diagram for gravity line “caterpillar” into a type IIB supergravity “ dragonfly” that is triggered by the inclusion of scalars and antisymmetric tensor fields. The final diagram corresponds to type IIB string theory E₈ global symmetry group, which is the subgroup of the conjectured E₁₁ hidden symmetry group. Application of the results for getting the type IIA/IIB T-duality rules and for searching for type IIB vacua solutions is considered.     

On the string interpretation of M(atrix) theory

It has been proposed recently that, in the framework of M(atrix) theory, = 8 supersymmetric U(N) Yang-Mills theory in 1 + 1 dimensions gives rise to type IIA long string configurations. We point out that the quantum moduli space of SYM_{1 + 1} gives rise to two quantum numbers, which fit very well into the M(atrix) theory. The two quantum numbers become familiar if one switches to a IIB picture, where they represent configurations of D-strings and fundamental strings. We argue that, due to the SL(2,Z) symmetry, of the IIB theory, such quantum numbers must represent configurations that are present also in the IIA framework.     

Superstring on pp-wave orbifold from large-N quiver gauge theory

We extend the proposal of Berenstein, Maldacena and Nastase to the Type IIB superstring propagating on a pp-wave over the R ⁴/Z _k orbifold. We show that first-quantized free string theory is described correctly by the large-N, fixed gauge coupling limit of [U(N)] ^k quiver gauge theory. We propose a precise map between gauge theory operators and string states for both untwisted and twisted sectors. We also compute leading-order perturbative correction to the anomalous dimensions of these operators. The result is in agreement with the value deduced from the string energy spectrum, thus substantiating our proposed operator-state map. Received: 14 March 2002 / Published online: 5 July 2002