Strings, Gauge Fields and Duality

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Strings, Gauge Fields and Duality

Содержание

2. The analytic S-matrix • O.A. Castro-Alvaredo, J. Dreißig and A. Fring, Integrable scattering theories with unstable
3. The bootstrap program (1978-... ) o) classical foreplay i) determination of the S-matrix ii) construction of
4. Scattering theory in 1+1 dim • factorization of the S-matrix:
5.  How does one construct S? • in general use perturbation theory • in 1+1 dim
7. • Examples for theories with real analytic S-matrices: - sine-Gordon: Al. B. Zamolodchikov, A. B. Zamolodchikov,
8. v) Yang-Baxter equation = • factorization • - no backscattering • diagonal S-matrix
9. vi) Fusing bootstrap equation = vii) Account for all poles - 2nd order pole Coleman-Thun mechanism
11. From form factors to correlation functions • Wightman’s reconstruction theorem: a QFT is solved once all
13. Q-H. Park, Phys. Lett. B328 (1994) 329 (cl.) T.J. Hollowood, J.L. Miramontes and Q-H. Park, Nucl.
14. Decoupling rule Example: SU(4)2-homogeneous sine-Gordon model P. Goddard, A. Kent, D.I. Olive, Unitary representations of the
15. How to detect unstable particles?
16. Particle spectrum: 6 stable particles 30 unstable particles 15 different masses + degeneracy depending on the
18. Скачать презентацию

Слайд 2

The analytic S-matrix
• O.A. Castro-Alvaredo, J. Dreißig and A. Fring, Integrable

scattering
theories with unstable particles, to appear J. of Euro. Phys. C (2004)
• O.A. Castro-Alvaredo, A. Fring, On vacuum energies and
renormalizability in integrable quantum field theories, hepth/0401075

Слайд 3

The bootstrap program (1978-... )
o) classical foreplay
i) determination of

the S-matrix
ii) construction of the form factors
iii) consistency checks
iv) correlation (Wightman) functions
v) classification of (local) operators
vi) organise the zoo of models
vii) add boundaries and impurities
viii) compute measurable quantities
ix) relate to lattice statistical models
x) interrelation of the program to
other areas (condensed matter)

Слайд 4

Scattering theory in 1+1 dim
• factorization of the S-matrix:

Слайд 5

 How does one construct S?
• in general use

perturbation theory

• in 1+1 dim IQFT: solve consistency equations

Слайд 6

Слайд 7

• Examples for theories with real analytic S-matrices:
- sine-Gordon:

Al. B. Zamolodchikov, A. B. Zamolodchikov, Annals Phys. 120, 253 (1979)
- affine Toda field theories:
R. Köberle, J. A. Swieca , Phys. Lett. B86, 209 (1979)
A. Arinshtein, V. Fateev, A.B. Zamolodchikov, Phys. Lett. B87, 389 (1979)
many papers in the early 90s, Corrigan et al, Mussardo et al, Freund et. al...
A.Fring, D.I. Olive; Nucl. Phys. B379, 429 (1992)
(possibly more on this in the next talk by Ed Corrigan),....

• Examples for theories with hermitian analytic S-matrices:
- homogeneous sine-Gordon:
J.L. Miramontes; Phys. Lett. B455, 231 (1999)
J.L. Miramontes, C. R. Fernandez-Pousa; Phys. Lett. B472, 392 (2000)
A. Fring, C. Korff, Phys. Lett. B477, 380 (2000)
C. Korff, Phys. Lett. B501, 289 (2001)

Слайд 8

v) Yang-Baxter equation
=
• factorization •
- no backscattering

• diagonal S-matrix

Слайд 9

vi) Fusing bootstrap equation
=
vii) Account for all poles
- 2nd

order pole Coleman-Thun mechanism

- higher order: generalised CT-mechanism

Слайд 10

Слайд 11

From form factors to correlation functions
• Wightman’s reconstruction theorem:
a

QFT is solved once all n-point functions are known

Слайд 12

Слайд 13

Q-H. Park, Phys. Lett. B328 (1994) 329 (cl.)
T.J. Hollowood, J.L. Miramontes

and Q-H. Park, Nucl. Phys. B445 (1995) 451 (cl.)
C.R. Fernández-Pousa, M.V. Gallas, T.J. Hollowood and J.L. Miramontes, Nucl. Phys. B484 (1997) 609 (cl.)
J.L. Miramontes and C.R. Fernández-Pousa, Phys. Lett. B472 (2000) 392 (S)
O.A. Castro-Alvaredo, A. Fring, C. Korff and J.L. Miramontes, Nucl. Phys. B575 (2000) 535 (TBA)
A. Fring and C. Korff, Phys. Lett. B477 (2000) 380 (S)
C. Korff, Phys. Lett. B501 (2001) 289 (S)
O.A. Castro-Alvaredo, A. Fring and C. Korff, Phys. Lett. B484 (2000) 167 (form factors)
O.A. Castro-Alvaredo and A. Fring, Nucl. Phys. B604 (2001) 367 (correlation functions)
O.A. Castro-Alvaredo and A. Fring, Phys. Rev. D63 (2001) 021701 (RG flow)
O.A. Castro-Alvaredo and A. Fring, Phys. Rev. D64 (2001) 085007 (form factors)

Theories with unstable particles generalities

D.I. Olive, N. Turok, The Symmetries of Dynkin diagrams and
the reduction of Toda field equations Nucl. Phys. B215 470 (1983)

For conformal field theory see review:
P. Goddard, D.I. Olive, Kac-Moody and Virasoro algebras
in relation to quantum physics Int. J Mod. Phys. A1, 303 (1986)

Слайд 14

Decoupling rule
Example: SU(4)2-homogeneous sine-Gordon model
P. Goddard, A. Kent, D.I. Olive,

Unitary representations of the
Virasoro algebra and Super-Virasoro Algebras CMP. 103, 105 (1986)

Слайд 15

How to detect unstable particles?

Слайд 16

Particle spectrum:
6 stable particles
30 unstable particles
15 different masses
+ degeneracy depending

on the choices of the sigmas

• TBA confirms all predictions •

Strings, Gauge Fields and Duality

Содержание

The analytic S-matrix• O.A. Castro-Alvaredo, J. Dreißig and A. Fring, Integrable

The bootstrap program (1978-... ) o) classical foreplay i) determination of

Scattering theory in 1+1 dim • factorization of the S-matrix:

 How does one construct S? • in general use

• Examples for theories with real analytic S-matrices: - sine-Gordon:

v) Yang-Baxter equation= • factorization • - no backscattering

vi) Fusing bootstrap equation= vii) Account for all poles- 2nd

From form factors to correlation functions • Wightman’s reconstruction theorem: a

Q-H. Park, Phys. Lett. B328 (1994) 329 (cl.)T.J. Hollowood, J.L. Miramontes

Decoupling rule Example: SU(4)2-homogeneous sine-Gordon modelP. Goddard, A. Kent, D.I. Olive,