Indian Physics Association Awards

Total Page:16

File Type:pdf, Size:1020Kb

Indian Physics Association Awards NEWS Following day, the participants moved the environment of deposition, litho- 2. Paliwal, B. S., J. Geol. Soc. India, 1998, to Sam, Jaisalmer. On the way they saw facies, structural set-up and microbial 52(1), 81–86. Pokaran Boulder Bed (PBB), considered life in the basin. Palaeontological data 3. Kumar, S. and Pandey, S. K., Curr. Sci., to be the base of MSG. Chauhan et al.5 need support from sedimentological in- 2008, 94, 1081–1085. and Bhatt et al.6 have discussed its origin puts. New macrofossil morpho-forms, 4. Kumar, S. and Pandey, S. K., J. Asian Earth Sci., 2010, 38, 77–85. and lithostratigraphic position. The ori- some of which are enigmatic, can give 5. Chauhan, D. S., Mathur, K. M. and Ram, gin of PBB, i.e. whether it is glacial important clues regarding early multicel- N., J. Geol. Soc. India, 2001, 58(5), 425– deposit or not, is being debated. Partici- lular organisms and their evolution. Fel- 433. pants were unanimous that there is no sic volcanic unit of Chhoti Khatu could 6. Bhatt, D. K., Prasad, S., Jain, R. L. and evidence to consider PBB as a glacial be significant and provide precise age Mathur, A. K., J. Geol. Soc. India, 2005, boulder bed. constraint for the basin. 65, 301–308. During the return journey to Jodhpur All participants appreciated the infor- participants saw the Malani Igneous mative, elegantly prepared field guide Suite in Baukan Section. The valedictory book and the meticulous planning of the session was held at Jodhpur. The oil in- field trip by the scientists from BSIP. S. K. Pandey* and Bandana Dimri, dustry was interested in the sequence Birbal Sahni Institute of Palaeobotany, stratigraphic framework of the MSG ba- 1. Raghav, K. S., De, C. and Jain, R. L., 53 University Road, Lucknow 226 007, sin which will be helpful to understand Indian Min., 2005, 59, 23–30. India. *e-mail: [email protected] Indian Physics Association Awards The Indian Physics Association Awards significant contributions in the areas of bai), for his significant contributions in 2012 were recently presented by M. K. hydrogen storage in nanomaterials and in the field of magnetism particularly in- Sanyal (President, Indian Physics Asso- the fields of non-crystallized solids. The volving neutron scattering. The award is ciation) at a function organized on 11 award carries a citation, gold medal and given for outstanding contributions in April 2014 at the Multipurpose Hall, cash prize of Rs 1 lakh. terms of innovative experimental tech- BARC Training School Hostel, Anushak- The Buti Foundation Award for 2012 niques or innovative instrumentation. tinagar, Mumbai. was given jointly to Aditi Sen De The award consists of a citation and a R. D. Birla Memorial Award 2012 was (Harish-Chandra Research Institute, cash prize of Rs 100,000. awarded jointly to T. V. Ramakrishnan Allahabad) for contributions to quantum Earlier awardees include, the Nobel (Indian Institute of Science (IISc), Ban- information, quantum optics and founda- Laureates Prof. Abdus Salam and Prof. galore) and Ajay Sood (IISc). Ramakrish- tions of quantum mechanics and V. K. S. Chandrasekhar among others are Prof. nan has made pioneering contributions in Chandrasekar (Bharathidasan University, A. Salam, Prof. B. V. Sreekantan, Prof. the theory of freezing of liquids and in Tiruchirappalli) for the understanding of Subrahmanyan Chandrasekhar, Prof. R. the localization of electrons due to disor- the fundamental aspects of nonlinear dy- Ramanna, Prof. Govind Swarup, Prof. der. Sood has researched in the areas of namics and complex systems. The award Sivaramakrishna Chandrasekhar, Dr. P. Raman spectroscopy and soft matter is given for outstanding contributions in K. Iyengar, Prof. R. Chidambaram, Prof. physics. The award is given once in two the area of theoretical applied physics, G. S. Agarwal, Prof. J. V. Narlikar, Prof. years for excellence in pure physics and astrophysics and biophysics. It carries a Ashoke Sen, Prof. Bikash Sinha and carries a citation, gold medal and cash citation, a gold medal and a cash prize of Prof. P. K. Kaw. prize of Rs 50,000. Rs 25,000. M. M. Chugani Memorial Award for The first P. K. Iyengar Memorial Parul R. Sheth, E-705/706 Kalp Nagri, excellence in applied physics for 2012 Award for excellence in experimental Vaishali Nagar, Mulund (West), Mumbai was awarded to O. N. Srivastava (Bana- physics was awarded to S. M. Yusuf 400 080, India. ras Hindu University, Varanasi) for his (Bhabha Atomic Research Centre, Mum- e-mail: [email protected] 170 CURRENT SCIENCE, VOL. 107, NO. 2, 25 JULY 2014 .
Recommended publications
  • Academic Report ( 2019–20 )
    Academic Report ( 2019–20 ) Harish - Chandra Research Institute Chhatnag Road, Jhunsi Prayagraj (Allahabad), India 211019 Contents 1. About the Institute 2 2. Director’s Report 4 3. List of Governing Council Members 5 4. Staff List 7 5. Academic Report - Mathematics 15 6. Academic Report - Physics 100 7. HRI Colloquia 215 8. Mathematics Talks and Seminars 216 9. Physics Talks and Seminars 218 10. Recent Graduates 222 11. Publications 224 12. Preprints 233 13. About the Computer Section 240 14. Library 242 15. Construction Activity 245 1 About The Institute History The Harish-Chandra Research Institute is one of the premier research institutes in the country. It is an autonomous institution fully funded by the Department of Atomic En- ergy (DAE), Government of India. The Institute was founded as the Mehta Research Institute of Mathematics and Mathematical Physics (MRI). On 10th Oct 2000 the In- stitute was renamed as Harish-Chandra Research Institute (HRI) after the acclaimed mathematician, the late Prof Harish-Chandra. MRI started with the efforts of Dr. B. N. Prasad, a mathematician at the University of Allahabad, with initial support from the B. S. Mehta Trust, Kolkata. Dr. Prasad was succeeded in January 1966 by Dr. S. R. Sinha, also of Allahabad University. He was followed by Prof. P. L. Bhatnagar as the first formal Director. After an interim period, in January 1983 Prof. S. S. Shrikhande joined as the next Director of the Institute. During his tenure the dialogue with the DAE entered into decisive stage and a review committee was constituted by the DAE to examine the Institute’s future.
    [Show full text]
  • Nominations for Different “Academy Awards/Lectures/ Medals”
    The National Academy of Sciences, India (NASI) 5, Lajpatrai Road, Prayagraj – 211002 Prof. Paramjit Khurana Ph.D., FNA, FASc, FNAAS, FTWAS, FNASc Prof. Satya Deo Ph.D. (Arkansas, USA), F.N.A.Sc. General Secretaries June 15, 2021 Subject : Nominations for different “Academy Awards/Lectures/Medals” Dear Fellows, I request you to kindly send nominations for the following “Academy Awards/Lectures/Medals”– 1. Prof. Meghnad Saha Memorial Lecture Award (2021) 2. Prof. N.R. Dhar Memorial Lecture Award (2021) 3. Prof. Archana Sharma Memorial Lecture Award (2021) 4. Prof. M.G.K. Menon Lecture Award (2021) 5. Prof. M.G.K. Menon Memorial Award (2021) 6. Prof. V. P. Sharma Memorial Lecture Award (2021) 7. Prof. A.K. Sharma Memorial Lecture Award (2021) 8. Prof. Prafulla Chandra Ray Memorial Lecture Award (2021) 9. Prof. S.K. Joshi Memorial Lecture Award (2021) 10. Prof. A.C. Banerji Memorial Lecture Award (2021) 11. Dr. B.P. Pal Memorial Lecture Award (2021) 12. Dr. P. Sheel Memorial (Young Women Scientist) Lecture Award (2021) 13. Prof. B.K. Bachhawat Memorial Lecture Award (2021) 14. Prof. U.S. Srivastava Memorial Lecture Award (2021) 15. Lecture Award in the field of Biodiversity (2021) 16. NASI-Buti Foundation Lecture Award (2021) The nomination papers duly completed in all respect should be emailed to NASI on [email protected] latest by July 15, 2021. No hard copy is required for this year; kindly send the nomination on aforesaid email only (not on any other email id of NASI). The copy of Regulations regarding these Academy Awards/Lectures/Medals and the names of past recipients are enclosed.
    [Show full text]
  • From 2D Droplets to 2D Yang-Mills Arxiv:2010.11923V1 [Hep-Th]
    Prepared for submission to JHEP From 2d Droplets to 2d Yang-Mills Arghya Chattopadhyaya, Suvankar Duttab, Debangshu Mukherjeeb;c, Neetub aInstitute of Mathematical Sciences, Homi Bhaba National Institute (HBNI) IV Cross Road, Taramani, Chennai 600113, Tamil Nadu, India bIndian Institute of Science Education and Research Bhopal Bhopal Bypass, Bhopal 462066, India cIndian Institute of Science Education and Research Thiruvananthapuram Vithura 695551, Kerala, India E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: We establish a connection between time evolution of free Fermi droplets and partition function of generalised q-deformed Yang-Mills theories on Riemann surfaces. Classical phases of (0 + 1) dimensional unitary matrix models can be characterised by free Fermi droplets in two dimensions. We quantise these droplets and find that the modes satisfy an abelian Kac-Moody algebra. The Hilbert spaces H+ and H− associated with the upper and lower free Fermi surfaces of a droplet admit a Young diagram basis in which the phase space Hamiltonian is diagonal with eigenvalue, in the large N limit, equal to the quadratic Casimir of u(N). We establish an exact mapping between states in H± and geometries of droplets. In particular, coherent states in H± correspond to classical deformation of upper and lower Fermi surfaces. We prove that correlation between two coherent states in H± is equal to the chiral and anti-chiral partition function of 2d Yang-Mills theory on a cylinder. Using the fact that the full Hilbert space H+ ⊗ H− admits a composite basis, we show that correlation between two classical droplet geometries is equal to the full U(N) Yang-Mills partition function on cylinder.
    [Show full text]
  • Academic Report ( 2018–19 )
    Academic Report ( 2018–19 ) Harish - Chandra Research Institute Chhatnag Road, Jhunsi Prayagraj (Allahabad), India 211019 Contents 1. About the Institute 2 2. Director’s Report 4 3. List of Governing Council Members 5 4. Staff list 6 5. Academic Report - Mathematics 15 6. Academic Report - Physics 100 7. HRI Colloquia 219 8. Mathematics Talks and Seminars 220 9. Physics Talks and Seminars 222 10. Recent Graduates 226 11. Publications 227 12. Preprints 236 13. About the Computer Section 242 14. Library 244 15. Construction Activity 247 1 About The Institute History: The Harish-Chandra Research Institute is one of the premier research in- stitutes in the country. It is an autonomous institution fully funded by the Department of Atomic Energy (DAE), Government of India. The Institute was founded as the Mehta Research Institute of Mathematics and Mathematical Physics (MRI). On 10th Oct 2000 the Institute was renamed as Harish-Chandra Research Institute (HRI) after the acclaimed mathematician, the late Prof Harish-Chandra. MRI started with the efforts of Dr. B. N. Prasad, a mathematician at the University of Allahabad, with initial support from the B. S. Mehta Trust, Kolkata. Dr. Prasad was succeeded in January 1966 by Dr. S. R. Sinha, also of Allahabad University. He was followed by Prof. P. L. Bhatnagar as the first formal Director. After an interim period, in January 1983 Prof. S. S. Shrikhande joined as the next Director of the Institute. During his tenure the dialogue with the DAE entered into decisive stage and a review committee was constituted by the DAE to examine the Institute’s future.
    [Show full text]
  • Annual Report
    THE INSTITUTE OF MATHEMATICAL SCIENCES C. I. T. Campus, Taramani, Chennai - 600 113. ANNUAL REPORT Apr 2003 - Mar 2004 Telegram: MATSCIENCE Fax: +91-44-2254 1586 Telephone: +91-44-2254 2398, 2254 1856, 2254 2588, 2254 1049, 2254 2050 e-mail: offi[email protected] ii Foreword I am pleased to present the progress made by the Institute during 2003-2004 in its many sub-disciplines and note the distinctive achievements of the members of the Institute. As usual, 2003-2004 was an academically productive year in terms of scientific publications and scientific meetings. The Institute conducted the “Fifth SERC School on the Physics of Disordered Systems”; a two day meeting on “Operator Algebras” and the “third IMSc Update Meeting: Automata and Verification”. The Institute co-sponsored the conference on “Geometry Inspired by Physics”; the “Confer- ence in Analytic Number Theory”; the fifth “International Conference on General Relativity and Cosmology” held at Cochin and the discussion meeting on “Field-theoretic aspects of gravity-IV” held at Pelling, Sikkim. The Institute faculty participated in full strength in the AMS conference in Bangalore. The NBHM Nurture Programme, The Subhashis Nag Memorial Lecture and The Institute Seminar Week have become an annual feature. This year’s Nag Memorial Lecture was delivered by Prof. Ashoke Sen from the Harish-Chandra Research Institute, Allahabad. The Institute has also participated in several national and international collaborative projects: the project on “Automata and concurrency: Syntactic methods for verification”, the joint project of IMSc, C-DAC and DST to bring out CD-ROMS on “The life and works of Srini- vasa Ramanujan”, the Xth plan project “Indian Lattice Gauge Theory Initiative (ILGTI)”, the “India-based neutrino observatory” project, the DRDO project on “Novel materials for applications in molecular electronics and energy storage devices” the DFG-INSA project on “The spectral theory of Schr¨odinger operators”, and the Indo-US project on “Studies in quantum statistics”.
    [Show full text]
  • Annual Report 2010 -11
    ANNUAL REPORT 2010 -11 INDIAN INSTITUTE OF SCIENCE EDUCATION & RESEARCH CET CAMPUS, THIRUVANANTHAPURAM - 695 016 Publication Committee Dr M.P. Rajan Dr S. Shankaranarayanan Dr Sujith Vijay Mr S Hariharakrishnan Mr B V Ramesh Technical Assistance: Ms. A. S. Aswathy Contact : 0471 2597459, Fax: 0471 2597427 Email : [email protected] CONTENTS Page No. Preface 1 Preamble Introduction 1 IISER Thiruvananthapuram Society 1 Board of Governors and other authorities 2 Academic Advisory Committee 3 2 Human Resource Faculty & their research profile 4 Administrative Support Personnel 20 Students (BS-MS & Ph.D Programme) 20 3 Academic Programmes 22 4 Research Activities Sponsored Projects 23 Fellowships 24 5 Research Publications 24 6 Awards and Honours 28 7 Other Academic Activities Faculty Activities Conferences & Workshops Attended 29 Invited Lectures /Seminars 31 Internship & Outreach Programme 33 Distinguished Visitors 33 Lectures, Colloquia & Seminars organized 34 8 Facilities Research Laboratories 40 Library Resources 40 Computing and Networking Facility 40 9 Sports and Cultural Activities 41 10 Permanent & Transit Campus 41 11 Statement of Audited Annual Account 44 i PREFACE Indian Institute of Science Education and Research Thiruvananthapuram, established by the Ministry of Human Resource Development, Government of India, in 2008 has completed three years. I am happy to present this report of the remarkable progress made by the institute in many fronts during the past year, with the aim of providing high quality education in modern science, integrating it with outstanding research at the undergraduate level itself. During this year we have doubled the faculty strength with one professor and fifteen assistant professors joining us. A brief description of the research interests of the faculty forms a part of this report.
    [Show full text]
  • Guwahati Annual Meeting
    No. 39 March 2004 Newsletter of the Indian Academy of Sciences Guwahati Annual Meeting The Academy held its 2003 annual meeting in Guwahati from 21 to 23 November at the invitation of the Indian Institute of Technology, Guwahati. This was the first time in sixty-nine years that the annual meeting was held in the north-east of the country. All the scientific sessions except a public lecture were held at Inside... the just-completed Senate Hall of IIT. Gautam Barua’s brief welcome address was followed by the traditional introduction of Fellows and Associates, a hundred of whom were present at Guwahati. K Kasturirangan, in his presidential address 2004 Elections on “Precision positioning: science and applications” talked about technologies New Fellows ............................... 4 Honorary Fellows ....................... 6 Council for the triennium 2004–06 ..................................... 6 Associates – 2003 ........................ 6 Raman Professor .......................... 7 Special issues of Journals ............ 7 behind satellite-based navigation systems and about their use in scientific studies, military and civilian applications such as for land, remote sensing, geo- Public Lectures ............................. 8 mapping, and in any application where the precise position in real time is to be determined. Discussion Meeting ...................... 10 The remaining programme of the three days was taken up by two symposia, two public lectures, two special lectures and 30-min presentations by eight new Refresher Courses........................ 10 Fellows and Associates. The first symposium was on nanomaterials and nanoscience, a truly interdisciplinary area encompassing physics, chemistry, biology, materials science and engineering. There has been tremendous interest Lecture Series ............................... 14 in this field in the last decade not only from the fundamental scientific point of view but also from possible technological applications in many areas.
    [Show full text]
  • Profiles and Prospects*
    Indian Journal of History of Science, 47.3 (2012) 473-512 MATHEMATICS AND MATHEMATICAL RESEARCHES IN INDIA DURING FIFTH TO TWENTIETH CENTURIES — PROFILES AND PROSPECTS* A K BAG** (Received 1 September 2012) The Birth Centenary Celebration of Professor M. C. Chaki (1912- 2007), former First Asutosh Birth Centenary Professor of Higher Mathematics and a noted figure in the community of modern geometers, took place recently on 21 July 2012 in Kolkata. The year 2012 is also the 125th Birth Anniversary Year of great mathematical prodigy, Srinivas Ramanujan (1887-1920), and the Government of India has declared 2012 as the Year of Mathematics. To mark the occasion, Dr. A. K. Bag, FASc., one of the students of Professor Chaki was invited to deliver the Key Note Address. The present document made the basis of his address. Key words: Algebra, Analysis, Binomial expansion, Calculus, Differential equation, Fluid and solid mechanics, Function, ISI, Kerala Mathematics, Kut..taka, Mathemtical Modeling, Mathematical Societies - Calcutta, Madras and Allahabad, Numbers, Probability and Statistics, TIFR, Universities of Calcutta, Madras and Bombay, Vargaprakr.ti. India has been having a long tradition of mathematics. The contributions of Vedic and Jain mathematics are equally interesting. However, our discussion starts from 5th century onwards, so the important features of Indian mathematics are presented here in phases to make it simple. 500-1200 The period: 500-1200 is extremely interesting in the sense that this is known as the Golden (Siddha–ntic) period of Indian mathematics. It begins * The Key Note Address was delivered at the Indian Association for Cultivation of Science (Central Hall of IACS, Kolkata) organized on behalf of the M.C.
    [Show full text]
  • Year Book of the Indian National Science Academy
    AL SCIEN ON C TI E Y A A N C A N D A E I M D Y N E I A R Year Book B of O The Indian National O Science Academy K 2019 2019 Volume I Angkor, Mob: 9910161199 Angkor, Fellows 2019 i The Year Book 2019 Volume–I S NAL CIEN IO CE T A A C N A N D A E I M D Y N I INDIAN NATIONAL SCIENCE ACADEMY New Delhi ii The Year Book 2019 © INDIAN NATIONAL SCIENCE ACADEMY ISSN 0073-6619 E-mail : esoffi [email protected], [email protected] Fax : +91-11-23231095, 23235648 EPABX : +91-11-23221931-23221950 (20 lines) Website : www.insaindia.res.in; www.insa.nic.in (for INSA Journals online) INSA Fellows App: Downloadable from Google Play store Vice-President (Publications/Informatics) Professor Gadadhar Misra, FNA Production Dr VK Arora Shruti Sethi Published by Professor Gadadhar Misra, Vice-President (Publications/Informatics) on behalf of Indian National Science Academy, Bahadur Shah Zafar Marg, New Delhi 110002 and printed at Angkor Publishers (P) Ltd., B-66, Sector 6, NOIDA-201301; Tel: 0120-4112238 (O); 9910161199, 9871456571 (M) Fellows 2019 iii CONTENTS Volume–I Page INTRODUCTION ....... v OBJECTIVES ....... vi CALENDAR ....... vii COUNCIL ....... ix PAST PRESIDENTS OF THE ACADEMY ....... xi RECENT PAST VICE-PRESIDENTS OF THE ACADEMY ....... xii SECRETARIAT ....... xiv THE FELLOWSHIP Fellows – 2019 ....... 1 Foreign Fellows – 2019 ....... 154 Pravasi Fellows – 2019 ....... 172 Fellows Elected (effective 1.1.2019) ....... 173 Foreign Fellows Elected (effective 1.1.2019) ....... 177 Fellowship – Sectional Committeewise ....... 178 Local Chapters and Conveners ......
    [Show full text]
  • Harish-Chandra Research Institute Academic Report ( 2003
    HARISH-CHANDRA RESEARCH INSTITUTE ACADEMIC REPORT ( 2003 - 2004 ) Chhatnag Road , Jhunsi , Allahabad - 211 019 , India CONTENTS 1. About the Institute 1 2. Director's Report 2 3. Governing Council 7 4. Academic Staff 9 5. Administrative Staff 12 6. Academic Report - Mathematics 14 7. Academic Report - Physics 37 8. Lectures , Talks & Seminars - Mathematics 93 9. Lectures , Talks & Seminars - Physics 95 10. Colloquium Jointly Organised by Maths and Physics 97 11. Publications & Preprints - Mathematics 98 12. Publications & Preprints - Physics 102 13. About the Library 111 14. About the Computer Section 112 15. Construction Work at the Campus 114 ABOUT THE INSTITUTE The Early Years Till 10th October 2000 the Institute was known as the Mehta Research Institute of Mathematics and Mathematical Physics (M.R.I). On 11.10.2000 it was renamed as Harish-Chandra Research Institute (H.R.I) after the mathematician, late Prof. Harish-Chandra. The Institute started with the efforts of Dr. B. N. Prasad, a mathematician at the University of Allahabad, who obtained the initial support from the B. S. Mehta Trust, Calcutta. Dr. Prasad was succeeded in January 1966 by Dr. S. R. Sinha, also of Allahabad University. He was followed by Prof. P. L. Bhatnagar, who joined as the first formal Director. On Prof. Bhatnagar's demise in October 1976, the responsibilities were again taken up by Dr. Sinha. In January 1983, Prof. S. S. Shrikhande of Bombay University joined as the next Director of the Institute. During his tenure the dialogue with the Department of Atomic Energy (DAE) en- tered into the decisive stage and a review committee was constituted by the DAE for examining the future of the Institute.
    [Show full text]
  • Ashoke Sen and S-Duality Winner of Fundamental Physics Prize
    GENERAL ¨ ARTICLE Ashoke Sen and S-Duality Winner of Fundamental Physics Prize Dileep Jatkar The Fundamental Physics Prize Foundation de- clared names of nine scientists in a varietyof ar- easof theoreticalphysicsas recipients of the Fun- damentalPhysicsPrize.Thisarticle is a quick introduction to Ashoke Sen's scienti¯c achieve- ments. In addition, this article containssome discussion of his S-duality proposal and the Sen Dileep Jatkar is a conjecture, which fetched him the Fundamental Professor at Harish- Physics Prize. Chandra Research Institute, Allahabad. He works in theoretical physics and his area of interest is string theory. The poor man says,\O King, both of us are Loknath; while I am theone whose masters are thepeople, you are master of thepeople". 1. Citation of the FundamentalPhysics Prize The year 2012 marks the beginning of the Fundamen- talPhysicsPrizefounded by Russianentrepreneur Yuri Milner. In the inauguralyear the Foundation announced a list of nine recipients for their outstanding contribu- tion to various disciplines in theoreticalphysics.Asper their website, http://fundamentalphysicsprize.org, TheFundamental Physics Prize recognizes transforma- tive advances in the ¯eldof fundamental physics ... in- cluding advances in closelyrelated ¯elds with deep con- nections tophysics. Ashoke Sen, a professor attheHarish-Chandra Research Keywords Institute, Allahabad, India is one of the nine recipients Fundamental Physics Prize of this Prize. The citation for which he is awarded this 2012, S-duality, Sen conjecture. RESONANCE ¨ April 2013 323 GENERAL ¨ ARTICLE Ashoke Sen prize (asstated onthewebsite) is received the [Ashoke Sen is awarded the Fundamental Physics Prize] Fundamental for uncovering strikingevidenceof strong-weakduality Physics Prize for in certain supersymmetric string theories andgauge the- providinga ories,opening thepath to therealization that all string definitiveevidence theories are di®erent limits of the same underlying in favour of S- theory.
    [Show full text]
  • Quantum Black Holes, Wall Crossing, and Mock Modular Forms Arxiv
    Preprint typeset in JHEP style - HYPER VERSION Quantum Black Holes, Wall Crossing, and Mock Modular Forms Atish Dabholkar1;2, Sameer Murthy3, and Don Zagier4;5 1Theory Division, CERN, PH-TH Case C01600, CH-1211, 23 Geneva, Switzerland 2Sorbonne Universit´es,UPMC Univ Paris 06 UMR 7589, LPTHE, F-75005, Paris, France CNRS, UMR 7589, LPTHE, F-75005, Paris, France 3NIKHEF theory group, Science Park 105, 1098 XG Amsterdam, The Netherlands 4Max-Planck-Institut f¨ur Mathematik,Vivatsgasse 7, 53111 Bonn, Germany 5Coll`egede France, 3 Rue d'Ulm, 75005 Paris, France Emails: [email protected], [email protected], [email protected] Abstract: We show that the meromorphic Jacobi form that counts the quarter-BPS states in N = 4 string theories can be canonically decomposed as a sum of a mock Jacobi form and an Appell-Lerch sum. The quantum degeneracies of single-centered black holes are Fourier coefficients of this mock Jacobi form, while the Appell-Lerch sum captures the degeneracies of multi-centered black holes which decay upon wall-crossing. The completion of the mock Jacobi form restores the modular symmetries expected from AdS3=CF T2 holography but has a holomorphic anomaly reflecting the non-compactness of the microscopic CFT. For every positive integral value m of the magnetic charge invariant of the black hole, our analysis leads arXiv:1208.4074v2 [hep-th] 3 Apr 2014 to a special mock Jacobi form of weight two and index m, which we characterize uniquely up to a Jacobi cusp form. This family of special forms and another closely related family of weight-one forms contain almost all the known mock modular forms including the mock theta functions of Ramanujan, the generating function of Hurwitz-Kronecker class numbers, the mock modular forms appearing in the Mathieu and Umbral moonshine, as well as an infinite number of new examples.
    [Show full text]