4,895 research outputs found
Polynomial Structures in One-Loop Amplitudes
A general one-loop scattering amplitude may be expanded in terms of master
integrals. The coefficients of the master integrals can be obtained from
tree-level input in a two-step process. First, use known formulas to write the
coefficients of (4-2epsilon)-dimensional master integrals; these formulas
depend on an additional variable, u, which encodes the dimensional shift.
Second, convert the u-dependent coefficients of (4-2epsilon)-dimensional master
integrals to explicit coefficients of dimensionally shifted master integrals.
This procedure requires the initial formulas for coefficients to have
polynomial dependence on u. Here, we give a proof of this property in the case
of massless propagators. The proof is constructive. Thus, as a byproduct, we
produce different algebraic expressions for the scalar integral coefficients,
in which the polynomial property is apparent. In these formulas, the box and
pentagon contributions are separated explicitly.Comment: 44 pages, title changed to be closer to content, section 2.1 extended
to section 2.1 and 2.2 to be more self-contained, references added, typos
corrected, the final version to appear in JHE
Counting Gauge Invariants: the Plethystic Program
We propose a programme for systematically counting the single and multi-trace
gauge invariant operators of a gauge theory. Key to this is the plethystic
function. We expound in detail the power of this plethystic programme for
world-volume quiver gauge theories of D-branes probing Calabi-Yau
singularities, an illustrative case to which the programme is not limited,
though in which a full intimate web of relations between the geometry and the
gauge theory manifests herself. We can also use generalisations of
Hardy-Ramanujan to compute the entropy of gauge theories from the plethystic
exponential. In due course, we also touch upon fascinating connections to Young
Tableaux, Hilbert schemes and the MacMahon Conjecture.Comment: 51 pages, 2 figures; refs updated, typos correcte
The Brane Box Model
An example of a non-Abelian Brane Box Model, namely one corresponding to a
orbifold singularity of \C^3, is constructed. Its
self-consistency and hence equivalence to geometrical methods are subsequently
shown. It is demonstrated how a group-theoretic twist of the non-Abelian group
circumvents the problem of inconsistency that arise from na\"{\i}ve attempts at
the construction.Comment: 27 Pages and 4 Figure
The Identity String Field and the Tachyon Vacuum
We show that the triviality of the entire cohomology of the new BRST operator
Q around the tachyon vacuum is equivalent to the Q-exactness of the identity I
of the star-algebra. We use level truncation to show that as the level is
increased, the identity becomes more accurately Q-exact. We carry our
computations up to level nine, where an accuracy of 3% is attained. Our work
supports, under a new light, Sen's conjecture concerning the absence of open
string degrees of freedom around the tachyon vacuum. As a by-product, a new and
simple expression for I in terms of Virasoro operators is found.Comment: 25 pages, 1 figure, references adde
Discrete Torsion, Covering Groups and Quiver Diagrams
Without recourse to the sophisticated machinery of twisted group algebras,
projective character tables and explicit values of 2-cocycles, we here present
a simple algorithm to study the gauge theory data of D-brane probes on a
generic orbifold G with discrete torsion turned on. We show in particular that
the gauge theory can be obtained with the knowledge of no more than the
ordinary character tables of G and its covering group G*. Subsequently we
present the quiver diagrams of certain illustrative examples of SU(3)-orbifolds
which have non-trivial Schur Multipliers. The paper serves as a companion to
our earlier work (arXiv:hep-th/0010023) and aims to initiate a systematic and
computationally convenient study of discrete torsion.Comment: 26 pages, 8 figures, some errors correcte
Orientifold dual for stuck NS5 branes
We establish T-duality between NS5 branes stuck on an orientifold 8-plane in
type I' and an orientifold construction in type IIB with D7 branes intersecting
at angles. Two applications are discussed. For one we obtain new brane
constructions, realizing field theories with gauge group a product of
symplectic factors, giving rise to a large new class of conformal N=1 theories
embedded in string theory. Second, by studying a D2 brane probe in the type I'
background, we get some information on the still elusive (0,4) linear sigma
model describing a perturbative heterotic string on an ADE singularity.Comment: 24 pages, LaTeX, references adde
Dimer Models from Mirror Symmetry and Quivering Amoebae
Dimer models are 2-dimensional combinatorial systems that have been shown to
encode the gauge groups, matter content and tree-level superpotential of the
world-volume quiver gauge theories obtained by placing D3-branes at the tip of
a singular toric Calabi-Yau cone. In particular the dimer graph is dual to the
quiver graph. However, the string theoretic explanation of this was unclear. In
this paper we use mirror symmetry to shed light on this: the dimer models live
on a T^2 subspace of the T^3 fiber that is involved in mirror symmetry and is
wrapped by D6-branes. These D6-branes are mirror to the D3-branes at the
singular point, and geometrically encode the same quiver theory on their
world-volume.Comment: 55 pages, 27 figures, LaTeX2
Toric Duality as Seiberg Duality and Brane Diamonds
We use field theory and brane diamond techniques to demonstrate that Toric
Duality is Seiberg duality for N=1 theories with toric moduli spaces. This
resolves the puzzle concerning the physical meaning of Toric Duality as
proposed in our earlier work. Furthermore, using this strong connection we
arrive at three new phases which can not be thus far obtained by the so-called
``Inverse Algorithm'' applied to partial resolution of C^3/Z_3 x Z_3. The
standing proposals of Seiberg duality as diamond duality in the work by
Aganagic-Karch-L\"ust-Miemiec are strongly supported and new diamond
configurations for these singularities are obtained as a byproduct. We also
make some remarks about the relationships between Seiberg duality and
Picard-Lefschetz monodromy.Comment: 33 pages and 15 figures; references added and some minor changes on
the remarks on Picard-Lefschetz theor
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