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Oindrila Ganguly Department of Physics University of Calcutta September 2016

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Oindrila Ganguly Department of Physics University of Calcutta September 2016 CORRECTEDCOPY LORENTZ INVARIANCE VIOLATION: A STUDY IN THE CONTEXTOFEFFECTIVETHEORIES Thesis submitted for the degree of Doctor of Philosophy (Science) in Physics (Theoretical) by oindrila ganguly Department of Physics University of Calcutta September 2016 LORENTZ INVARIANCE VIOLATION: A STUDY IN THE CONTEXTOFEFFECTIVETHEORIES oindrila ganguly An Exploration of Spacetime Symmetries September 2016 Oindrila Ganguly: Lorentz invariance violation: A study in the context of effective theories, An Exploration of Spacetime Symmetries, © Septem- ber 2016 “You give much and know not that you give at all." — Khalil Gibran, ‘The Prophet’ Dedicated to Tattu, who taught me to look beyond. ABSTRACT Exact invariance of spacetime under Lorentz boosts, whether it be lo- cal or global, corresponds to a scale free nature of spacetime, locally or globally, because arbitrarily high boosts expose extremely short dis- tances. It is possible that spacetime has a short distance cutoff of the order of the Planck length lPl and consequently a preferred frame! A novel microscopic structure of spacetime should then emerge at such resolutions. Yet, till date, there is no complete theory that can explain physics near the Planck scale, reproduce our observable low energy world consistently and make experimentally verifiable pre- dictions. However, there is a strong support for the hypothesis that Planck scale physics can induce observable violation of Lorentz invari- ance. An effective field theory based phenomenological model by My- ers and Pospelov breaks boost invariance in flat spacetime through a modified Lagrangian density with new Planck suppressed third or- der derivative terms characterised by a constant background vector. This leads to modified non linear dispersion relations with cubic con- tributions to the momentum. In such theories of Lorentz violation, we 1 identify a fairly general class of field configurations (of spins 0, 2 and 1) which preserve invariance under infinitesimal Lorentz transforma- tions and also satisfy equations of motion yielding cubic dispersion relations similar to those found earlier. These restricted fields are de- fined as functions of the fixed background vector in such a way that background dependence of the dynamics of the physical system is not manifest. We demonstrate that these fields can provide a field ba- sis for the realisation of Lorentz algebra and allow the construction of a Poincaré invariant symplectic two form on the covariant phase space of the theory. Lorentz non invariant theories may alternatively be modelled by analogue systems. Sound waves in a classical, irrotational, barotropic, inviscid fluid propagate like scalar fields in a curved Lorentzian ge- ometry. But if the fluid is viscous, Lorentz invariance of the analogue spacetime is destroyed. A draining bathtub flow gives rise to an ana- logue spacetime qualitatively similar to the spacetime outside a Kerr black hole. Theoretically, acoustic superradiance or superresonance has previously been shown to occur here. We explore how acoustic Lorentz violation due to dispersive and dissipative effects of viscos- ity affects superresonance from this fluidic analogue of a rotating ax- isymmetric black hole. We also discuss avenues of improvement of our result and possible diversification to other systems. vii Lorentz invariance violation: A study in the context of effective theories Oindrila Ganguly Abstract Exact invariance of spacetime under Lorentz boosts, whether it be local or global, corresponds to a scale free nature of spacetime , locally or globally, because arbitrarily high boosts expose extremely short distances. It is pos- sible that spacetime has a short distance cutoff of the order of the Planck length lP l and consequently a preferred frame! A novel microscopic structure of spacetime should then emerge at such resolutions. Yet, till date, there is no complete theory that can explain physics near the Planck scale, reproduce our observable low energy world consistently and make experimentally veri- fiable predictions. However, there is a strong support for the hypothesis that Planck scale physics can induce observable violation of Lorentz invariance. An effective field theory based phenomenological model by Myers and Pospelov breaks boost invariance in flat spacetime through a modified La- grangian density with new Planck suppressed third order derivative terms characterised by a constant background vector. This leads to modified non linear dispersion relations with cubic contributions to the momentum. In such theories of Lorentz violation, we identify a fairly general class of field 1 configurations (of spins 0; 2 and 1) which preserve invariance under infinites- imal Lorentz transformations and also satisfy equations of motion yielding cubic dispersion relations similar to those found earlier. These restricted fields are defined as functions of the fixed background vector in such a way that background dependence of the dynamics of the physical system is not manifest. We demonstrate that these fields can provide a field basis for the realisation of Lorentz algebra and allow the construction of a Poincar´e invariant symplectic two form on the covariant phase space of the theory. 1 PUBLICATIONS Some of the research leading to this thesis have appeared previously in the following publications: Journal articles [1] Oindrila Ganguly. ‘A realisation of Lorentz algebra in Lorentz violating theory’. In: Eur. Phys. J. C72 (2012), p. 2209. doi: 10. 1140/epjc/s10052-012-2209-5. arXiv: 1206.1695 [hep-th]. [2] Oindrila Ganguly, Debashis Gangopadhyay, and Parthasarathi Majumdar. ‘Lorentz-preserving fields in Lorentz-violating the- ories’. In: Europhys.Lett. 96 (2011), p. 61001. doi: 10.1209/0295- 5075/96/61001. arXiv: 1011.1206 [hep-th]. Conference proceedings [3] Oindrila Ganguly, Debashis Gangopadhyay, and Parthasarathi Majumdar. ‘A discussion on Lorentz preserving scalar fields in Lorentz violating theory’. In: Proceedings, International Confer- ence on Modern Perspectives of Cosmology and Gravitation (COS- GRAV 12). Vol. 405. 2012, p. 012015. doi: 10.1088/1742-6596/ 405/1/012015. ix Your hearts know in silence the secrets of the days and the nights. But your ears thirst for the sound of your heart’s knowledge. You would know in words that which you have always known in thought. You would touch with your fingers the naked body of your dreams. — Khalil Gibran, ‘The Prophet’ ACKNOWLEDGMENTS Here ends the journey begun many years ago with a lot of hope but no path in sight. A narrow way emerged somehow, and brought me to the present day when I am penning down my acknowledgements for my PhD thesis. I am still only a novice and have the same wonder at everything I see, as when I embarked on this journey, but may be am a little bit more mature. I thank everyone who have participated in and shared the travails of this expedition. Firstly, I owe my parents heartfelt gratitude for letting me live my dream. I know that I have tested their patience by managing to be re- markably unsuccessful compared to everyone around me! So, it must have taken a lot of effort from them to keep faith and stand by me. I thank my supervisor, Prof. Debashis Gangopadhyay, for being supportive, patient and lenient. Every discussion with him used to be an invigorating experience, as I came back laden with more diverse information than I had originally gone looking for. He is very strict about the duties of students but is at the same time concerned about their fair treatment. His straight forward attitude is admirable I thank Prof. Parthasarathi Majumdar, my joint supervisor, for be- ing a wonderful advisor, teacher and friend to me. To refer to him just as my joint supervisor is misleading. Our association dates back to 2003, when I first heard him lecture at the ‘Summer School’ or- ganised by Indian Association for the Cultivation of Science, Kolkata. He is one of the best teachers I have ever come across. No one can probably inspire me and make me realise my abilities like him. But I must have been his most exasperating student, not as obedient as he would have liked me to be. Yet, I respect him sincerely and I shall always remain thankful for having him as one of my advisors. Here, I should also mention my heartfelt gratitude to my thesis commit- tee members, specially Prof. Soumitra Sengupta for his critical inputs and innovative suggestions. I thank Tamoghna for being my friend. He has worked tirelessly from the very beginning for our dream mission, Aloha, an initiative to protect the native Indian dogs. He has always believed in me and also spoilt me by attending to my odd wishes. He is a person I can rely on in difficult times. Though Nirupam has requested me not to, I thank Nirupam for coming back to India and easing responsibilities xi off me just to help me concentrate on my doctoral studies. He has been what a friend is meant to be. I loved to discuss physics with him and enjoyed it the most when starting from some simple little physics problem, we eventually got stuck somewhere and then spent hours sorting things out. He also participated enthusiastically with me in my work on analogue gravity, digging up various ingenious ideas to resolve the complications. I shall not thank him any more because, I do not know how to. There is my sister, who must be reading this to check whether I have said nice and proper things about her. Yes, I do thank Mitthi earnestly for always pestering me about approaching deadlines. But, most importantly, in spite of her young age, she took upon herself a number of responsibilities to make my life smooth. Without her help I would have found it difficult to carry on. In this regard, I am also grateful to Gaurab, Surasree, Aryadeep and Anirban. I am indebted to my institute Satyendra Nath Bose National Cen- tre for Basic Sciences (SNBNCBS), Kolkata for providing a beautiful natural environment for students to pursue their studies in.
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