1. Anomalous U(1)΄s, Chern-Simons couplings and the Standard Model Pascal Anastasopoulos (INFN, Roma “Tor Vergata”) Pascal Anastasopoulos (INFN, Roma “Tor Vergata”) Alessandria, 15 December 2006 Work in collaboration with: Massimo Bianchi, Emilian Dudas, Elias Kiritsis. Work in collaboration with: Massimo Bianchi, Emilian Dudas, Elias Kiritsis.

2. Anomalous U(1)΄s are a generic prediction of all open string models (possible candidates to describe Standard Model). The anomaly is cancelled via Green-Schwarz-Sagnotti mechanism, and the anomalous U(1)΄s become massive. However, generalized Chern-Simons couplings are necessary to cancel all the anomalies. These Chern-Simons terms provide new signals that distinguish such models from other Z΄-models. Such couplings may have important experimental consequences. Content of this lecture

3. Therefore under : Anomalous U(1) ΄ s If, the U(1) is anomalus and gauge symmetry is broken due to the 1-loop diagram: which also transforms as:, therefore: To cancel the anomaly we add an axion: and the anomaly is cancelled. Consider a chiral gauge theory:

4. Anomalous U(1) ΄ s are massive The axion which mixes with the anomalous U(1)΄s is a bulk field emerging from the twisted RR sector. The term that mixes the axion with the U(1) gives mass to the gauge boson and breaks the U(1) symmetry: The UV mass can be computed from a string 1-loop diagram.

5. Limits of the open 1-loop diagrams The mass is the UV contact term: The β-function Antoniadis Bachas Dudas Antoniadis Kiritsis Rizos The convergent part provides the threshold corrections. UV limit IR limit Antoniadis Bachas Dudas, Bianchi Trevigne, Anastasopoulos Bianchi Sarkissian Stanev (To appear) RR-fields

6. where s is a bulk modulus. In SUSY models, they are the chiral partners of the axions. If we are on the O-pane, and the global U(1) symmetry remains intact. Anomalous U(1) ΄ s and F-I terms The masses of the anomalous U(1)s are proportional to the internal volumes. If D the brane where the U(1) is attached and P the O-pane where the axion is localized: There are D-term like potentials of the form: Poppitz D-brane O-plane

7. Consider now the presence of an additional non-anomalous U(1). By definition, this means that: Presence of non-anomalous U(1) ΄ s However, there might be mixed anomalies due to the traces: break the gauge symmetries: Diagrams of the following type:

8. However, the axionic transformation does not cancel all the anomalies. The above action is -gauge invariant. The need of Chern-Simons terms To cancel the anomalies we add axions as before: We need non-invariant terms: Generalized Chern – Simons. ? ?

9. Chern-Simons terms To cancel the anomalies we obtain: We need non-invariant terms: Now, a combination of the axionic and the GCS-terms cancel the anomalies: The anomalies fix the coefficients of the GCS-terms in the effective action. the variation

10. The General Case It is easy to show that: E ~ Consider the general Lagrangian:

11. General Anomaly Cancellation Special Cases: No fermions. Only one anomalous U(1). Requiring: under and, the anomaly cancellation conditions are:

12. String Computation of GCS The GCS-terms are:

13. An example: The Z Orientifold We compactify the 6 extra dimensions: After tadpole cancellation, the gauge group and the massless spectum are: 6 T 2 T 2 T 2 we identify points: 4D

14. An example: The Z Orientifold 6 Among them, 4 are anomalous and 2 non-anomalous. However, 5 become massive and 1 remains massless. (due to higher dimensional anomalies) Ibanez Marchesano Rabadan, Antoniadis Kiritsis Rizos, Anastasopoulos In this model, there are six U(1)΄s. Gauge group: U(6) × U(6) × U(4)| × U(6) × U(6) × U(4)| 95

15. An example: The Z Orientifold Therefore, if where: is not zero, 6 E ijj ~ we do need generalised GCS-terms to cancel all the anomalies: Chern-Simons terms are necessary. This is a generic property of all orientifold models.

16. ~ ~ Heavy Fermions GCS-terms are also a prediction of an anomaly-free chiral gauge theory with heavy and light fermions (after SSB). Denoting the heavy mass-insertion with ( × ): example:

17. ~ ~ Heavy Fermions GCS-terms are also a prediction of an anomaly-free chiral gauge theory with heavy and light fermions (after SSB). Denoting the heavy mass-insertion with ( × ): example: Therefore, we end-up with a chiral gauge theory with light ferimons, axions and GCS-terms.

18. Phenomenological implications SU(3) × SU(2) × U(1) Y Standard Model There are three more abelian gauge bosons. These U(1)΄s are anomalous. A typical D-brane description of the Standard Model (Top Down or Bottom Up): SU(3) × SU(2) × U(1) × U(1) × U(1) × U(1)΄ 32 Aldazabal Ibanez Marchesano Quevedo Rabadan Uranga, Cvetic Shiu, Blumenhagen Honecker Kors Lust Ott, Antoniadis Dimopoulos Kiritsis Tomaras Rizos, Schellekens et al..

19. D-branes & Gauge Groups Adjoint U(m) SU(m) x U(1) m (m,-1| n,+1) - mn (m,+1| n,+1) m n Set of representations: Adjoints, bifundamentals, antisymmetric & symmetric. (Antisym,+2) m

20. A low string scale model Higgses are charged under Y and PQ but not under B and L. After EW symmetry breaking, both Y and PQ are spontaneously broken. Two origins for masses: 1. 1. The UV mass matrix of the anomalous U(1)s: ~ M s. 2. 2. The Higgs mechanism: v H ~ 100-200 GeV. Antoniadis Tomaras Kiritsis Rizos

21. Z-Z ΄ Mixings We go to the photon basis: The coefficients are:

22. CS Couplings and LHC Consider the various anomaly canceling GCS-terms : Coriano Irges Kiritsis Some terms are zero on-shell. Therefore, new signals may be visible in LHC, like:

23. Conclusions Anomalous U(1)΄s are a generic prediction of orientifold vacua. If the string scale is low (few TeV region) such gauge bosons become the tell-tales signals of such vacua. Anomaly related Chern Simons-like couplings produce new signals that distinguish such models from other Z΄- models. Such signals may be visible in LHC.