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1.1 The Research Activities/Conformance with the Work Programme

   Task VI:

   In accordance with the Work Programme and time schedule important
   results were obtained within the subtasks 1 and 2 by the Contractor 4.

   Due to appearance of new ideas in string theory
   some deviations from the work program (Contractor 4) took place and
   results that were
   not expected at the stage of application of the proposal were obtained.

1.2. Scientific results

The main obtained results include:

   Task VI.

Noncommutative analogs of scalar electrodynamics and N=2 D=4 SUSY
Yang-Mills theory were considered (Contractor 4). It has been
shown that one-loop renormalizability of noncommutative scalar
electrodynamics requires the scalar potential to be an
anticommutator squared. This form of the scalar potential differs
from the one expected from the point of view of noncommutative
gauge theories with extended SUSY containing a square of
commutator. It has been shown that fermion contributions restore
the commutator in the scalar potential. This provides one-loop
renormalizability of noncommutative N=2 SUSY gauge theory. A
presence of non-integrable IR singularities in noncommutative
scalar electrodynamics for general coupling constants was
demonstrated. It was found that for a special ratio of coupling
constants these IR singularities vanish. Also it has been shown
that IR poles are absent in noncommutative N=2 SUSY gauge theory.
(Ref 4.1, 4.3)

Results that were not expected at the stage of application
(Contractor 4):

The conjecture that at the stationary point of the tachyon
potential for the non-BPS D-brane or brane-anti-D-brane pair of
superstring theories the negative energy density cancels the brane
tension was tested using a cubic superstring field theory with
insertion of a double-step inverse picture changing operator. The
tachyon potential on levels 1 and 4 was calculated and accounted
for 97.5\% and 99.2\% of the expected vacuum energy respectively
(Ref. 4.4).

A globally consistent treatment of linearized gravity in the
Randall-Sundrum background with matter on the brane has been
formulated. Using a novel gauge, in which the transverse
components of the metric are non-vanishing the gauge symmetries
were analysed. These results underline the necessity for
non-gravitational confinement of matter to the brane. Linearized
gravity  in the thick brane version of the Randall-Sundrum
background has been also considered. It has been found that the
axial gauge ($h_{55}=h_{5\mu}=0$) is inconsistent in the presence
of matter on the thick brane. Also it has been shown that
linearized gravity is different from an expected form to reproduce
the linearized Einstein gravity on a slice of the thick brane
(Ref. 4.2, 4.5).

2.  List of publications that contain acknowledgments to INTAS.

Publications without of INTAS-NIS co-authorship of the project
teams.

International journals

4.1. I. Ya. Aref'eva, D. M. Belov, A. S. Koshelev, O. A. Rytchkov,
Renormalizability and UV/IR Mixing in Noncommutative theories with
Scalar Fields, Phys.Lett.B 487(2000)357, hep-th/0003276, 0001215.

4.2. I. Ya. Aref'eva, M. G. Ivanov, W. Mueck, K. S. Viswanathan,
  I. V. Volovich, "Consistent Linearized Gravity in Brane Backgrounds"
  Nucl.Phys. B590 (2000) 273-286, hep-th/0004114

Published in proceedings

4.3. Ya. Aref'eva, D. M. Belov, A. S. Koshelev, O. A. Rytchkov,
UV/IR Mixing for Noncommutative  Field Theories. To be published
in proceedings of the conference dedicated to the memory of Prof.
D.V.Volkov (invited talk).

4.4. Ya. Aref'eva, D. M. Belov, A. S. Koshelev, P. B. Medvedev
Tachyon condensation in cubic superstring field theory,
hep-th/0011117, in Proceedings of the International Conference
"Quantization, Gauge Theory and Strings", dedicated to the memory
of Prof. Efim Fradkin, Moscow, Russia, June 5-10, 2000 (invited
talk).

4.5. I. Ya. Aref'eva, M. G. Ivanov, W. Mueck, K. S. Viswanathan,
  I. V. Volovich, "Linearized Gravity  on Thick Branes"
  To be published in proceedings of International Seminar
  "Quarks-2000" (invited talk).


3. Meetings and visits under this INTAS project
  (when, where, what was done, output, budget spent
   from the INTAS funds).

 From May 15 till May 20, 2000,
I.Ya. Aref'eva participated in the International Seminar
"Quarks-2000", Pushkin, Russia, where the talk entitled
"Non-perturbative effects in string field theory" was presented.
From September 9 till September 15, 2000, I.Ya. Aref'eva
participated in the European Research Conference on Particle
Physics and Gravitation, Greece. From January 3 till January 12,
2001, A.S. Koshelev and O.A. Rytchkov participated in the
conference "Strings 2001", Tata Institute, Mumbai, India. From
April 1 till April 15, 2001, A.S. Koshelev participated in the
"Workshop on superstrings and related matters", ICTP, Trieste,
Italy. From May 15 till May 20, 2000, O.A. Rytchkov participated
in the International Seminar "Quarks-2000", Pushkin, Russia, where
the talk entitled "Renormalization and UV/IR mixing in
non-commutative field theories" was presented. From July 2 till
July 8, 2000 I.V. Volovich participated in the Ninth Marcel
Grossman Meeting, Rome, Italy, where the talk entitled "Consistent
Linearized Gravity in Brane Backgrounds" was presented.


The total travel support for the visits of I.A. Aref'eva was 1155
EURO.

The total travel support for the visits of A.S. Koshelev was 300
EURO.

The total travel support for the visits of O.A. Rytchkov was 190
EURO.

The total travel support for the visits of I.V. Volovich was 450
EURO.

4. Problems (if any).

    ANNEXES

    RESULTS

    Results of Steklov Mathematical Institute team:

M1. Noncommutative analogs of scalar electrodynamics and N=2 D=4
SUSY Yang-Mills theory were considered. It has been shown that
one-loop renormalizability of noncommutative scalar
electrodynamics requires the scalar potential to be an
anticommutator squared. This form of the scalar potential differs
from the one expected from the point of view of noncommutative
gauge theories with extended SUSY containing a square of
commutator. It has been shown that fermion contributions restore
the commutator in the scalar potential. This provides one-loop
renormalizability of noncommutative N=2 SUSY gauge theory. A
presence of non-integrable IR singularities in noncommutative
scalar electrodynamics for general coupling constants was
demonstrated. It was found that for a special ratio of coupling
constants these IR singularities vanish. Also it has been shown
that IR poles are absent in noncommutative N=2 SUSY gauge theory.
(I. Ya. Aref'eva, A. S. Koshelev, O. A. Rytchkov)

M2. It has been conjectured that at the stationary point of the
tachyon potential for the non-BPS D-brane or brane-anti-D-brane
pair of superstring theories, the negative energy density cancels
the brane tension. This conjecture for a cubic superstring field
theory with insertion of a double-step inverse picture changing
operator has been studied. The tachyon potential on levels 1 and 4
was computed and accounted for 97.5\% and 99.2\% of the expected
vacuum energy respectively (I. Ya. Aref'eva, A. S. Koshelev)

M3. A globally consistent treatment of linearized gravity in the
Randall-Sundrum background with matter on the brane has been
formulated. Using a novel gauge, in which the transverse
components of the metric are non-vanishing, the brane is kept
straight. The gauge symmetries and physical degrees of freedom
were analyzed. These results underline the necessity for
non-gravitational confinement of matter to the brane. (I. Ya.
Aref'eva, I. V. Volovich)

M4. Linearized gravity  in the thick brane version of the
Randall-Sundrum background has been considered. It was found that
the axial gauge ($h_{55}=h_{5\mu}=0$) is inconsistent in the
presence of matter on the thick brane. A new gauge with
nonvanishing transverse components of the metric for weak
gravitational field was used. It was shown that linearized gravity
is different from an expected form to reproduce the linearized
Einstein gravity on a slice of the thick brane. To perform a thin
brane limit one has to make an extra 5-dimensional gauge
transformation, that restores the linearized Einstein gravity on
the thin brane. (I. Ya. Aref'eva, I. V. Volovich)

 List of team members and problems solved by each
member:

1. I. Ya. Aref'eva, M1, M2, M3, M4

2. A. S. Koshelev, M1, M2

3. O. A. Rytchkov, M1

4. I. V. Volovich, M3, M4

Give the obtained funding beyond labour costs.

Travel: 2095 EURO

Equipment: 1550 EURO

Other Costs: 465 EURO

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