string theory, Fall_2000
https://services.math.duke.edu/mcal?listgroup-5
String theory Upcoming Seminarsen-us2024-03-29T09:53:03-04:00https://services.math.duke.edu/mcal2024-01-01T12:00:00-05:002dailyA New Perspective on Calabi-Yau Geometry
https://services.math.duke.edu/mcal?abstract-3507
Work over the past few years by Mark Gross, Ilya Zharkov, and Wei-Dong Ruan
has led to a clear conjectural picture for the structure of generic
supersymmetric T^3 fibrations on Calabi-Yau threefolds. We will explain
this picture, show how mirror symmetry would be a natural consequence
of it, and discuss other possible applications.David Morrison (Duke University)2000-08-31T16:30:00-04:003507string theoryString Theory SeminarFall, 2000Thu, 31 Aug 2000 16:30:00 EDTThursday, August 31, 2000, 4:30pm120 PhysicsThu, 31 Aug 2000 17:30:00 EDTA New Perspective on Calabi-Yau Geometry, II
https://services.math.duke.edu/mcal?abstract-3508
Work over the past few years by Mark Gross, Ilya Zharkov, and Wei-Dong Ruan
has led to a clear conjectural picture for the structure of generic
supersymmetric T^3 fibrations on Calabi-Yau threefolds. We will explain
this picture, show how mirror symmetry would be a natural consequence
of it, and discuss other possible applications.David Morrison (Duke University)2000-09-07T16:30:00-04:003508string theoryString Theory Seminar120 PhysicsThu, 07 Sep 2000 17:30:00 EDTThursday, September 7, 2000, 4:30pmFall, 2000Thu, 07 Sep 2000 16:30:00 EDTThe Zero-Brane as a Soliton
https://services.math.duke.edu/mcal?abstract-3493
We present an exact construction of the D0-brane as a soliton on the
worldvolume of a BPS D2-brane in the presence of a large B field.
We match the mass and spectrum of fluctuations of this soliton to the
D0-D2 conformal field theory. This spectrum includes a tachyon:
the endpoint of tachyon condensation represents the ``disappearance''
of the D0-brane, and all modes associated with it, as it dissolves in the
D2-brane. This construction thus sheds some light on issues related
to tachyon condensation.<a href="mailto:millerpd@umich.edu">Peter Miller</a> (University of Michigan)2000-09-14T16:30:00-04:003493string theoryString Theory SeminarThu, 14 Sep 2000 17:30:00 EDT120 PhysicsThursday, September 14, 2000, 4:30pmFall, 2000Thu, 14 Sep 2000 16:30:00 EDTM theory and twisted K theory
https://services.math.duke.edu/mcal?abstract-3510
The talk will be focused on the relation between K theory and M theory
and it's generalization to nonzero $B$ field. The main idea is a
comparison of the long distance partition functions of the two theories.
In the process we will outline a derivation of the (twisted) Atiyah -
Hirzebruch spectral sequence from M theory. We will also discuss
the relation between $SL(2,Z)$ duality and K theory.Duiliu-Emanuel Diaconescu (Institute for Advanced Study)2000-09-21T16:30:00-04:003510string theoryString Theory SeminarThursday, September 21, 2000, 4:30pmFall, 2000Thu, 21 Sep 2000 16:30:00 EDTThu, 21 Sep 2000 17:30:00 EDT120 PhysicsBrane World: A New Scenario of Our Universe
https://services.math.duke.edu/mcal?abstract-3545
The recent exciting scenario that matter is confined to a brane while
gravity lives in higher dimensions is introduced and reviewed.
Experimental and cosmological tests will be discussed.<a href="http://www.physics.cornell.edu/physics/PROF.PAGES/TyeH.html">Henry Tye</a> (Cornell University)2000-09-22T16:00:00-04:003545string theoryUNC Physics and Astronomy ColloquiumFri, 22 Sep 2000 17:00:00 EDTPhillips Hall (UNC-CH) room 215Fall, 2000Fri, 22 Sep 2000 16:00:00 EDTFriday, September 22, 2000, 4:00pmNoncommutative Geometry and Yang-Mills Symmetry
https://services.math.duke.edu/mcal?abstract-3543
<a href="http://www.physics.unc.edu/directory/index.phtml?area=99&mode=n&sstring=11">Louise Dolan</a> (University of North Carolina, Chapel Hill)2000-09-28T16:30:00-04:003543string theoryString Theory Seminar at UNC-CHThursday, September 28, 2000, 4:30pmFall, 2000Thu, 28 Sep 2000 16:30:00 EDT265 Phillips Hall (UNC-CH)Thu, 28 Sep 2000 17:30:00 EDTConsistency of Z_M Orbifold Conformal Field Theories on K3
https://services.math.duke.edu/mcal?abstract-3550
Katrin Wendland (UNC-CH)2000-10-12T16:30:00-04:003550string theoryString Theory Seminar at UNC-CHThursday, October 12, 2000, 4:30pmThu, 12 Oct 2000 16:30:00 EDTFall, 2000Phillips Hall (UNC-CH)Thu, 12 Oct 2000 17:30:00 EDTWarped Compactifications on Calabi-Yau Fourfolds
https://services.math.duke.edu/mcal?abstract-3552
Motivated by phenomenological applications we consider (warped)
compactifications of type IIA string theory on Calabi-Yau fourfolds in
the presence of Ramond-Ramond fluxes. The main goal of the talk is a
description of low-energy physics, including a new superspace formulation
of two-dimensional N = (2,2) dilaton supergravity coupled to
matter, and computation of the effective superpotentials induced by
fluxes.Sergei Gukov (Caltech & Princeton University)2000-10-26T16:30:00-04:003552string theoryString Theory Seminar120 PhysicsThu, 26 Oct 2000 17:30:00 EDTFall, 2000Thu, 26 Oct 2000 16:30:00 EDTThursday, October 26, 2000, 4:30pmN=1 Gauge Theory and Warped Deformed Conifold
https://services.math.duke.edu/mcal?abstract-3569
We revisit the singular IIB supergravity solution describing M fractional
3-branes on the conifold (hep-th/0002159). Its 5-form flux decreases,
which we explain by showing that the relevant N=1 SUSY SU(N+M) x SU(N)
gauge theory undergoes repeated Seiberg-duality transformations in which
N -> N-M. Far in the IR the gauge theory confines; its chiral
symmetry breaking removed the singularity of hep-th/0002159 by
deforming the conifold. We propose a non-singular pure-supergravity
background dual to the field theory on all scales, with small curvature
everywhere if the 't Hooft coupling (g_s M) is large.
In the UV it approaches that of hep-th/0002159, incorporating the
logarithmic flow of couplings. In the IR the deformation of the conifold
gives a geometrical realization of chiral symmetry breaking and confinement.
We suggest that pure N=1 Yang-Mills may be dual to strings propagating at
small (g_s M) on a warped deformed conifold. We note also that the
standard model itself may lie at the base of a duality cascade.<a href="http://PUPGG.PRINCETON.EDU/www/jh/research/Klebanov_Igor.htmlx">Igor Klebanov</a> (Princeton University)2000-11-02T16:30:00-05:003569string theoryString Theory Seminar120 PhysicsThu, 02 Nov 2000 17:30:00 ESTFall, 2000Thu, 02 Nov 2000 16:30:00 ESTThursday, November 2, 2000, 4:30pmElements of D-Geometry
https://services.math.duke.edu/mcal?abstract-3560
We present a framework for the study of D-branes on Calabi-Yau
compactifications, valid throughout moduli space. The main elements of
this framework are the identification of D-branes as objects in a category,
and a new notion of stability. We apply these ideas to the study of
the spectrum of BPS branes on a specific Calabi-Yau and the algebra of
BPS states.<a href="http://www.physics.rutgers.edu/people/pips/Fiol.html">Bartomeu Fiol</a> (Rutgers University)2000-11-09T16:30:00-05:003560string theoryString Theory SeminarThursday, November 9, 2000, 4:30pmThu, 09 Nov 2000 16:30:00 ESTFall, 2000Thu, 09 Nov 2000 17:30:00 EST120 PhysicsThe principle of functorialty: an elementary introduction
https://services.math.duke.edu/mcal?abstract-3571
The principle of functoriality is a central question in present day
mathematics. It is a far reaching, but quite precise, conjecture of
Langlands that relates fundamental arithmetic information with equally
fundamental analytic information. The arithmetic information arises
from the solutions of algebraic equations. It includes data that
classify algebraic number fields, and more general algebraic varieties.
The analytic information arises from spectra of differential equations
and group representations. It includes data that classify irreducible
representations of reductive groups. The lecture will be a general
introduction to these things. If time permits, we shall also describe
recent progress that is being made on the problem.<a href="http://www.math.toronto.edu/">Jim Arthur</a> (University of Toronto)2000-11-16T16:00:00-05:003571geometry/topologyalgebraic geometrystring theoryColloquiumThu, 16 Nov 2000 16:00:00 ESTFall, 2000Thursday, November 16, 2000, 4:00pm120 PhysicsThu, 16 Nov 2000 17:00:00 ESTProof of the Penrose Inequality Using the Positive Mass Theorem
https://services.math.duke.edu/mcal?abstract-3566
We prove the Riemannian Penrose conjecture, an important case of a
conjecture made by Roger Penrose in 1973, by defining a new flow of metrics.
This flow of metrics stays inside the class of
asymptotically flat Riemannian 3-manifolds with nonnegative scalar curvature
which contain minimal spheres.
In particular, if we consider a
Riemannian 3-manifold as a totally geodesic submanifold of a space-time
in the context of general relativity, then outermost minimal spheres
with total area <I>A</I>
correspond to apparent horizons of black holes
contributing a mass <IMG WIDTH="75" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
SRC="faculty/saper/Images/bray1/img1.gif"
ALT="$\sqrt{A/16\pi}$">, scalar curvature
corresponds to local energy density at each point, and the rate at which
the metric becomes flat at infinity corresponds to total mass. The
Riemannian Penrose conjecture then states
that the total mass of an
asymptotically flat 3-manifold with nonnegative scalar curvature
is greater than or equal to the mass contributed by the black holes.
<p>
The flow of metrics we define continuously evolves the original 3-metric
to a Schwarzschild 3-metric, which represents a spherically
symmetric black hole in vacuum. We define the flow such that the
area of the minimal spheres (which flow outward) and hence
the mass contributed by the black holes
in each of the metrics in the flow is constant, and then use the positive
mass theorem to show that the total mass of the
metrics is nonincreasing. Then since the total mass equals the mass of the
black holes in a Schwarzschild metric, the Riemannian Penrose conjecture
follows.<a href="http://www-math.mit.edu/people/faculty/bray.html">Hubert Bray</a> (M.I.T.)2000-11-20T16:00:00-05:003566geometry/topologyalgebraic geometrystring theoryGeometry/Topology SeminarMonday, November 20, 2000, 4:00pmFall, 2000Mon, 20 Nov 2000 16:00:00 EST216 PhysicsMon, 20 Nov 2000 17:00:00 ESTVolume Comparison Theorems Involving Scalar Curvature
https://services.math.duke.edu/mcal?abstract-3575
Bishop's theorem says that an <I>n</I>-manifold, <IMG WIDTH="49" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="faculty/saper/Images/bray2/img1.gif"
ALT="$n \ge 2$">,
with Ricci curvature greater than
that of the standard, round <I>n</I>-sphere has less total volume. It is then
natural to ask whether or not this is true for scalar curvature as well.
The answer, however, is no for <IMG WIDTH="49" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="faculty/saper/Images/bray2/img2.gif"
ALT="$n \ge 3$">,
which can be seen by considering the cross
product metric on <IMG WIDTH="81" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
SRC="faculty/saper/Images/bray2/img3.gif"
ALT="$S^{n-1} \times {\bf R}$">, which can be scaled to have
arbitrarily large scalar curvature and yet infinite volume.
<P>
However, this counterexample metric is quite far from the standard, round
metric on <I>S</I><SUP><I>n</I></SUP>, and it turns out that for metrics sufficiently close to the
standard metric <I>g<SUB>0</SUB></I> on <I>S<SUP>3</SUP></I>,
greater scalar curvature does imply less
total volume. To be precise, suppose (<I>M<SUP>3</SUP></I>,<I>g</I>) has scalar curvature
<IMG WIDTH="112" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
SRC="faculty/saper/Images/bray2/img4.gif"
ALT="$R(g) \ge R(g_0)$"> and Ricci curvature <IMG WIDTH="141" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
SRC="faculty/saper/Images/bray2/img5.gif"
ALT="$Ric(g) \ge \epsilon Ric(g)$">.(Notice that this condition is equivalent to the hypothesis of Bishop's theorem
for <IMG WIDTH="45" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="faculty/saper/Images/bray2/img6.gif"
ALT="$\epsilon = 1$"> but is weaker for <IMG WIDTH="45" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="faculty/saper/Images/bray2/img7.gif"
ALT="$\epsilon < 1$">.) Then we prove that
there exists an <IMG WIDTH="83" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
SRC="faculty/saper/Images/bray2/img8.gif"
ALT="$\epsilon_0 \in (0,1)$"> such that for all
<IMG WIDTH="82" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
SRC="faculty/saper/Images/bray2/img9.gif"
ALT="$\epsilon \in [\epsilon_0, 1],$"> the total volume <IMG WIDTH="143" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
SRC="faculty/saper/Images/bray2/img10.gif"
ALT="$Vol(g) \le Vol(g_0)$">.Furthermore, using techniques involving isoperimetric surfaces (surfaces which
minimize area given a volume constraint), we are able to derive an explicit
formula for the optimal value of <IMG WIDTH="17" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
SRC="faculty/saper/Images/bray2/img11.gif"
ALT="$\epsilon_0$">, which we note is between 0.134
and 0.135. More generally, we find that for any <IMG WIDTH="75" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
SRC="faculty/saper/Images/bray2/img12.gif"
ALT="$\epsilon \in (0,1)$">,
<IMG WIDTH="176" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
SRC="faculty/saper/Images/bray2/img13.gif"
ALT="$Vol(g) \le \lambda(\epsilon) Vol(g_0)$">, and we compute the <IMG WIDTH="36" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
SRC="faculty/saper/Images/bray2/img14.gif"
ALT="$\lambda(\epsilon)$">which makes the inequality sharp. It is interesting to note that for
<IMG WIDTH="81" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
SRC="faculty/saper/Images/bray2/img15.gif"
ALT="$\epsilon \in (0,\epsilon_0)$">, the Riemannian manifold with maximal volume
is best described as a ``football metric,'' which approaches a cylinder in the
limit as <IMG WIDTH="10" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
SRC="faculty/saper/Images/bray2/img16.gif"
ALT="$\epsilon$"> goes to zero.<a href="http://www-math.mit.edu/people/faculty/bray.html">Hubert Bray</a> (M.I.T.)2000-11-22T13:00:00-05:003575geometry/topologyalgebraic geometrystring theoryGeometry/Topology Seminar120 PhysicsWed, 22 Nov 2000 14:00:00 ESTWednesday, November 22, 2000, 1:00pmFall, 2000Wed, 22 Nov 2000 13:00:00 ESTNo talk today -- Thanksgiving break
https://services.math.duke.edu/mcal?abstract-3546
Mary Pugh (University of Pennsylvania)2000-11-23T16:00:00-05:003546string theoryString Theory SeminarThursday, November 23, 2000, 4:00pmThu, 23 Nov 2000 16:00:00 ESTFall, 2000120 PhysicsThu, 23 Nov 2000 17:00:00 ESTThe Finite-N AdS/CFT correspondence for Pedestrians
https://services.math.duke.edu/mcal?abstract-3594
<a href="http://www.physics.unc.edu/~frampton/home.html">Paul Frampton</a> (UNC-CH)2000-11-27T16:00:00-05:003594string theoryUNC Theoretical Physics and Astrophysics SeminarMonday, November 27, 2000, 4:00pmMon, 27 Nov 2000 16:00:00 ESTFall, 2000258 Phillips Hall (UNC-CH)Mon, 27 Nov 2000 17:00:00 ESTFluctuations of the Giant Graviton
https://services.math.duke.edu/mcal?abstract-3581
Gravitons moving in AdS_m x S^n spacetimes along the S^n blow up into
spherical (n-2) branes whose radius increases with increasing angular
momentum. This leads to an upper bound on the angular momentum providing
an implementation of the ``stringy exclusion principle.'' We show that
this bound is present only for states which saturate a BPS-like condition
involving the energy E and angular momentum J, E <= J/R, where R is the
radius of S^n. Restriction of motion to such states lead to a
noncommutativity of the coordinates on S^n. As an example of motions which
do not obey the exclusion principle bound, we show that there are finite
action instanton configurations interpolating between two possible
BPS states. We suggest that this is consistent with the proposal that
there is an effective description in terms of supergravity on a
noncommutative space and noncommutativity arises here because of imposing
supersymmetry. Quantum fluctations of the giant graviton are also
discussed.<a href="http://www.het.brown.edu/people/antal/index.html">Antal Jevicki</a> (Brown University)2000-11-30T16:30:00-05:003581string theoryString Theory Seminar at UNC-CHThursday, November 30, 2000, 4:30pmThu, 30 Nov 2000 16:30:00 ESTFall, 2000Thu, 30 Nov 2000 17:30:00 ESTPhillips Hall (UNC-CH)