112 research outputs found
Courant algebroid connections and string effective actions
Courant algebroids are a natural generalization of quadratic Lie algebras,
appearing in various contexts in mathematical physics. A connection on a
Courant algebroid gives an analogue of a covariant derivative compatible with a
given fiber-wise metric. Imposing further conditions resembling standard
Levi-Civita connections, one obtains a class of connections whose curvature
tensor in certain cases gives a new geometrical description of equations of
motion of low energy effective action of string theory. Two examples are given.
One is the so called symplectic gravity, the second one is an application to
the the so called heterotic reduction. All necessary definitions, propositions
and theorems are given in a detailed and self-contained way.Comment: Proceedings of Tohoku Forum for Creativity, Special volume:
Noncommutative Geometry and Physics I
Nonabelian bundle 2-gerbes
We define 2-crossed module bundle 2-gerbes related to general Lie 2-crossed
modules and discuss their properties. A 2-crossed module bundle 2-gerbe over a
manifold is defined in terms of a so called 2-crossed module bundle gerbe,
which is a crossed module bundle gerbe equipped with an extra sructure. It is
shown that string structures can be described and classified using 2-crossed
module bundle 2-gerbes.Comment: Further correction
Differential calculus on quantum groups: constructive procedure
A brief review of the construction and classifiaction of the bicovariant differential calculi on quantum groups is given
Non-Commutative GUTs, Standard Model and C,P,T
Noncommutative Yang-Mills theories are sensitive to the choice of the
representation that enters in the gauge kinetic term. We constrain this
ambiguity by considering grand unified theories. We find that at first order in
the noncommutativity parameter \theta, SU(5) is not truly a unified theory,
while SO(10) has a unique noncommutative generalization. In view of these
results we discuss the noncommutative SM theory that is compatible with SO(10)
GUT and find that there are no modifications to the SM gauge kinetic term at
lowest order in \theta.
We study in detail the reality, hermiticity and C,P,T properties of the
Seiberg-Witten map and of the resulting effective actions expanded in ordinary
fields. We find that in models of GUTs (or compatible with GUTs) right-handed
fermions and left-handed ones appear with opposite Seiberg-Witten map.Comment: 28 pages. Added references and comments in the introductio
The Standard Model on Non-Commutative Space-Time
We consider the Standard Model on a non-commutative space and expand the
action in the non-commutativity parameter theta. No new particles are
introduced, the structure group is SU(3) x SU(2) x U(1). We derive the leading
order action. At zeroth order the action coincides with the ordinary Standard
Model. At leading order in theta we find new vertices which are absent in the
Standard Model on commutative space-time. The most striking features are
couplings between quarks, gluons and electroweak bosons and many new vertices
in the charged and neutral currents. We find that parity is violated in
non-commutative QCD. The Higgs mechanism can be applied. QED is not deformed in
the minimal version of the NCSM to the order considered.Comment: 28 pages, v3: typos corrected, new appendix on alternative kinetic
terms for gauge bosons; v4: typos correcte
The Noncommutative Standard Model and Forbidden Decays
In this contribution we discuss the Noncommutative Standard Model and the
associated Standard Model-forbidden decays that can possibly serve as an
experimental signature of space-time noncommutativity.Comment: 15 pages, 1 figure, Invited talk at 9th Adriatic Meeting and Central
European Symposia on Particle Physics and The Universe, Dubrovnik, Croatia,
4-14 Sep 200
Anomaly freedom in Seiberg-Witten noncommutative gauge theories
We show that noncommutative gauge theories with arbitrary compact gauge group
defined by means of the Seiberg-Witten map have the same one-loop anomalies as
their commutative counterparts. This is done in two steps. By explicitly
calculating the \epsilon^{\m_1\m_2\m_3\m_4} part of the renormalized
effective action, we first find the would-be one-loop anomaly of the theory to
all orders in the noncommutativity parameter \theta^{\m\n}. And secondly we
isolate in the would-be anomaly radiative corrections which are not BRS
trivial. This gives as the only true anomaly occurring in the theory the
standard Bardeen anomaly of commutative spacetime, which is set to zero by the
usual anomaly cancellation condition.Comment: LaTeX 2e, no macros, no figures, 32 A4 page
Effective Field Theories on Non-Commutative Space-Time
We consider Yang-Mills theories formulated on a non-commutative space-time
described by a space-time dependent anti-symmetric field .
Using Seiberg-Witten map techniques we derive the leading order operators for
the effective field theories that take into account the effects of such a
background field. These effective theories are valid for a weakly
non-commutative space-time. It is remarkable to note that already simple models
for can help to loosen the bounds on space-time
non-commutativity coming from low energy physics. Non-commutative geometry
formulated in our framework is a potential candidate for new physics beyond the
standard model.Comment: 22 pages, 1 figur
Non-Commutative GUTs, Standard Model and C,P,T properties from Seiberg-Witten map
Noncommutative generalizations of Yang-Mills theories using Seiberg-Witten
map are in general not unique. We study these ambiguities and see that SO(10)
GUT, at first order in the noncommutativity parameter \theta, is unique and
therefore is a truly unified theory, while SU(5) is not. We then present the
noncommutative Standard Model compatible with SO(10) GUT. We next study the
reality, hermiticity and C,P,T properties of the Seiberg-Witten map and of
these noncommutative actions at all orders in \theta. This allows to compare
the Standard Model discussed in [5] with the present GUT inspired one.Comment: 9 pages. Presented at the Balkan Workshop 2003, Vrnjacka Banja,
29.8-2.9.2003 and at the 9th Adriatic Meeting, Dubrovnik, 4-14.9.200
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