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arXiv:1001.0428v2 [hep-ph] 11 Jun 2010 Symmetry, Integrability and Geometry: Methods and Applications SIGMA 6 (2010), 049, 29 pages Finite Unification: Theory and Predictions ⋆ Sven HEINEMEYER † 1 , Myriam MONDRAG ´ ON † 2 and George ZOUPANOS † 3 † 4 † 1 Instituto de F´ ısica de Cantabria (CSIC-UC), Santander, Spain E-mail: [email protected] † 2 Instituto de F´ ısica, Universidad Nacional Aut´onoma de M´ exico, Apdo. Postal 20-364, M´ exico 01000, M´ exico E-mail: myriam@fisica.unam.mx † 3 Theory Group, Physics Department, CERN, Geneva, Switzerland E-mail: [email protected] † 4 Physics Department, National Technical University, 157 80 Zografou, Athens, Greece Received January 03, 2010, in final form May 25, 2010; Published online June 11, 2010 doi:10.3842/SIGMA.2010.049 All-loop Finite Unified Theories (FUTs) are very interesting N = 1 supersym- metric Grand Unified Theories (GUTs) which not only realise an old field theoretic dream but also have a remarkable predictive power due to the required reduction of couplings. The reduction of the dimensionless couplings in N = 1 GUTs is achieved by searching for renormalization group invariant (RGI) relations among them holding beyond the unification scale. Finiteness results from the fact that there exist RGI relations among dimensionless couplings that guarantee the vanishing of all beta-functions in certain N = 1 GUTs even to all orders. Furthermore developments in the soft supersymmetry breaking sector of N =1 GUTs and FUTs lead to exact RGI relations, i.e. reduction of couplings, in this dimension- ful sector of the theory too. Based on the above theoretical framework phenomenologically consistent FUTS have been constructed. Here we present FUT models based on the S U (5) and S U (3) 3 gauge groups and their predictions. Of particular interest is the Higgs mass prediction of one of the models which is expected to be tested at the LHC. Key words: unification; gauge theories; finiteness; reduction of couplings 2010 Mathematics Subject Classification: 81T60; 81V22 1 Introduction A large and sustained effort has been done in the recent years aiming to achieve a unified description of all interactions. Out of this endeavor two main directions have emerged as the most promising to attack the problem, namely, the superstring theories and non-commutative geometry. The two approaches, although at a different stage of development, have common unification targets and share similar hopes for exhibiting improved renormalization properties in the ultraviolet (UV) as compared to ordinary field theories. Moreover the two frameworks came closer by the observation that a natural realization of non-commutativity of space appears in the string theory context of D-branes in the presence of a constant background antisymmetric field [1]. Among the numerous important developments in both frameworks, it is worth noting two conjectures of utmost importance that signal the developments in certain directions in string theory and not only, related to the main theme of the present review. The conjectures refer to ? T h i s p a p e r i s a c o n t r i b u t i o n t o t h e P r o c e e d i n g s o f t h e E i g h t h I n t e r n a t i o n a l C o n f e r e n c e \ S y m m e t r y i n N o n l i n e a r M a t h e m a t i c a l P h y s i c s " ( J u n e 2 1 { 2 7 , 2 0 0 9 , K y i v , U k r a i n e ) . T h e f u l l c o l l e c t i o n i s a v a i l a b l e a t h t t p : / / w w w . e m i s . d e / j o u r n a l s / S I G M A / s y m m e t r y 2 0 0 9 . h t m l

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Page 1: JUNIOR PROGRAMMES 2019 - ZUMA Education€¦ · New York & East Coast Tour Fordham University & East Coast Tour New York, USA Our junior language programme at Fordham University &

zumaeducation.com

JUNIOR PROGRAMMES 2019

Page 2: JUNIOR PROGRAMMES 2019 - ZUMA Education€¦ · New York & East Coast Tour Fordham University & East Coast Tour New York, USA Our junior language programme at Fordham University &

Innovative Teaching Approach

Vibrant International Environment

Truly Spectacular Locations

Page 3: JUNIOR PROGRAMMES 2019 - ZUMA Education€¦ · New York & East Coast Tour Fordham University & East Coast Tour New York, USA Our junior language programme at Fordham University &

ABOUT ZUMAZUMA Education offers an innovative and unique learning experience which incorporates a specialised language programme, tailored to the specific needs of students and the environment around them. Our programmes are aimed at students wanting to learn English while having a memorable summer being immersed in the most spectacular locations in the world.

Truly Spectacular Locations

Amazing Cultural Programme

Page 4: JUNIOR PROGRAMMES 2019 - ZUMA Education€¦ · New York & East Coast Tour Fordham University & East Coast Tour New York, USA Our junior language programme at Fordham University &

New York

Fordham University

Age11-18

New York, USA

• 15 hours tuition per week• Qualified and experienced native speaker teachers • Maximum of 15 students per class• Course materials and certificate

TUITION PROGRAMME

• Metro card & New York city pass• Daily excursions to New York• New York Yankees baseball match• Varied evening activities programme

ACTIVITIES & EXCURSIONS

• Double twin bedrooms with ensuite bathroom• Breakfast, lunch and dinner• Two dinners out a week including Hard Rock Cafe

FULL BOARD & ACCOMMODATION

Our junior language programme at Fordham University is available for 11 - 18 year old students and combines English lessons in the morning with an exciting cultural and activity programme in the afternoon and evening.

Page 5: JUNIOR PROGRAMMES 2019 - ZUMA Education€¦ · New York & East Coast Tour Fordham University & East Coast Tour New York, USA Our junior language programme at Fordham University &

New York &East Coast Tour

Fordham University & East Coast Tour New York, USAOur junior language programme at Fordham University & East Coast Tour is designed for 11 - 18 year old students and offers one week in New York with an adapted English course and a full excursion programme to key attractions. The second week includes a fantastic tour by private bus to explore the most beautiful natural wonders and the greatest influential historical sites of the East Coast of the United States.

• 30 hours language tuition in the first week • Qualified and experienced native speaker teachers• Maximum of 15 students• Course materials and certificate

TUITION PROGRAMME

• Metro card & daily excursions to New York • 6 days/5 nights bus trip to Niagara Falls, Washington, Amish Country and Philadelphia• Entrance to Maid of the Mist & excursion to Jersey Gardens

ACTIVITIES & EXCURSIONS

• Double twin bedrooms with ensuite bathroom • Accommodation in hotel during the tour• Breakfast, lunch and dinner • Breakfast in hotel during the tour

FULL BOARD & ACCOMMODATION

Age11-18

Page 6: JUNIOR PROGRAMMES 2019 - ZUMA Education€¦ · New York & East Coast Tour Fordham University & East Coast Tour New York, USA Our junior language programme at Fordham University &

San Diego

San Diego State University

Age13-18

San Diego, USAOur junior language programme at San Diego State University is available for 13 - 18 year old students and combines English lessons in the morning with an exciting cultural and activity programme in the afternoon and evening.

• 15 hours tuition per week• Qualified and experienced native speaker teachers • Maximum of 15 students per class• Course materials and certificate

TUITION PROGRAMME

• Trolley pass & daily excursions to San Diego• Excursion to Westfield Outlet• Full day excursion to Los Angeles• San Diego Harbour Cruise

ACTIVITIES & EXCURSIONS

• Two double twin bedrooms with ensuite bathroom• Breakfast, lunch and $10 voucher for dinner• Two dinners out a week including Hard Rock Cafe

FULL BOARD & ACCOMMODATION

Page 7: JUNIOR PROGRAMMES 2019 - ZUMA Education€¦ · New York & East Coast Tour Fordham University & East Coast Tour New York, USA Our junior language programme at Fordham University &

San Diego &West Coast Tour

San Diego State University & West Coast Tour San Diego, USAOur junior language programme at San Diego State University & West Coast Tour is designed for 13 - 18 year old students and offers one week in San Diego with an adapted English course and a full excursion programme to key attractions. The second week includes a fantastic tour by private bus to explore the most beautiful natural wonders and the greatest influential historical sites of the West Coast of the United States.

• 30 hours language tuition in the first week • Qualified and experienced native speaker teachers• Maximum of 15 students• Course materials and certificate

TUITION PROGRAMME

• Trolley pass & daily excursions to San Diego • 6 days/5 nights trip to Hoover Dam, Las Vegas, Los Angeles and San Francisco• Entrance to Hoover Dam & excursion to Westfield Outlet

ACTIVITIES & EXCURSIONS

• Two double twin bedrooms with ensuite bathroom • Accommodation in hotel during the tour• Breakfast, lunch and $10 voucher for dinner • Breakfast in hotel during the tour

FULL BOARD & ACCOMMODATION

Age13-18

Page 8: JUNIOR PROGRAMMES 2019 - ZUMA Education€¦ · New York & East Coast Tour Fordham University & East Coast Tour New York, USA Our junior language programme at Fordham University &

zumaeducation.com

ZUMA EDUCATION207 Regent StreetLondonW1B 3HHUnited Kingdom

Tel: +44 (0) 207 043 2269Fax: +44 (0) 207 043 [email protected]


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