Phase structure of Topologically massive gauge theory with fermion - - PowerPoint PPT Presentation

phase structure of topologically massive gauge theory
SMART_READER_LITE
LIVE PREVIEW

Phase structure of Topologically massive gauge theory with fermion - - PowerPoint PPT Presentation

Phase structure of Topologically massive gauge theory with fermion by spectral function Yuichi Hoshino,KNCT,7/21,Panasonic Yukawa Hall ! "# $%&'(#$&)*' &+ ,-.+#/0123)#4'( '5 ! "#$ %&&'(& )* +#,-./0,1$23'-4 5'%1


slide-1
SLIDE 1

Phase structure of Topologically massive gauge theory with fermion by spectral function Yuichi Hoshino,KNCT,7/21,Panasonic Yukawa Hall

slide-2
SLIDE 2
slide-3
SLIDE 3

! "# $%&'(#$&)*' &+ ,-.+#/0123)#4'( '5

! "#$ %&&'(& )* +#,-./0,1$23'-4 5'%1 !! " "!6 #$#!$ ! % " ! % " "!#& # !!&"!$&#'( ' " )#* # '$ !+ ( ) " ,! (+- 7 8/$3(/&. 29::'2&2 ;%#3$3&* 35 <.,#' 1':3,5= 8 >?@A2';'1' 35B1%1'$ $3;'1:'5-'2 <3&. (%22#'22 C.,&,5/ . -91'$ )* ;%-99( C,#%13D%&3,56&&/ %CC1,E3(%&3,56 F GHIAJ.'15/K3(,5 %5$ L52&%5&,5 'M'-&2 (,$3B* %,(%/ #,92 $3('523,5= N J/K/ $'C'5$'5-' ,B O'1(3,5 (%22 32 %229('$ &, )' 2(%##= P

!

00

"

$ " 12324, ,1 % B,1 7 %5$ F/2C35,1=

=

slide-4
SLIDE 4

! "#$%&'(#%#) *+,,-%.#)

!"#$#% &$$&'"() *+$" (,$(-%&. .+%( +/ 0#/$ /+%12.&- 34 .#*5(%(-14 $"(#-(0 !! " !"##$ $ %% " & $ ' #$ $ %%& ! '& &()(#%* +% # '()#"#% $ $% " ,%-#$* .%/ 678 0##&% /9('$-&. :2%'$+#% 1 +/ 1+;(% 1 "

!

2*% #&3%&4#%&%5#%+% '()#"% " ,%

"

+*6

!!!!/ 6<8 =% $"+/ '&/( $"( /9('$-&. :2%'$+#% 7 +/ 1+;(% 7#8% "

!

2*, '()#!"8 " ,%'()#!' $,$% ,3$,$ '()#1%/ 6>8

slide-5
SLIDE 5

!"#$% &'#$($'#$') *"+,

!

!"#

$!$ ! " !%#$& " ' ( % !&' (# $' " )&# % ! $' " )& % * ! ! )# (+

  • ./

012%32)&"' "* ,

  • )!"#$%$&' ()*+,-.

.$*&

, $/&% "

"

*+) 0$#1&#2$)# ! -#&3$)*& ,-.$0) " /& " ,-.$!- #/#& /10 #/# " /01 , " 0%#(#

" $

*

4*4.,$/ % 4'& ! %#

" $

*

*4.,$/ % 4'& ! 0%#$* ! !& 5 5-#.,$/&+ /21 3" 4)&"(&' (%5& #,$ 6"!*& -" , !5 7$!**&" %5 , " ! %# /1$,-.$!- #/#&

  • !#/# 01$- #/#&&!

%# /1 % '# 01$- #/#&

slide-6
SLIDE 6

!!! ! "# "$ "%#$ &'(!!$ "%"#& '$ ) ($& !"# $%&'& *+!)# )

! #

"

&'(!!)*# * !*& !(# *+!$ "%"# ) !+ ! ,-!$ "%"# . !$ "%"# . ,!$$#- !)# *+' ,%& -&./012 +'/&' 01 $ $& %.3& ., 4%+', /04,.15& . ) !" . !#"$ "%#$ . "$+ /#( . "$ /#( ,-!$ "%"# . "$ /# "%" ,-!$ "%"# ! "$ "%# "%" !! . " ! $+#- !6# $%&'& + 04 78-&'94 5+14,.1, .1/ ( 04 . :%;405.- <.44= (/!%# ) ( &'(!!( "%"# 0# "%" &'(!.# !>?#

slide-7
SLIDE 7

!"#$# %& '(&& &"%)* (+, %*& -./ 0.$$#0*%.+ !!!"! " ## $$!"! %&'% !"!( " ## )*$!"!'& + ) " #'(( 1223 ,-.')( %& 4($('#*$%5#, %+ *"# ).--.6%+/ ).$' ,-.')( " *'% !"!(++,!"!- 1273 * " ,-.' '## $$! + ## )*$%'& + )((- + " ## $$!- , " ## $$(8(9/# %+:($%(+*; 12<3 ) !"#$ #% "&!'() *%+), %- !"! !'. /!$$01- + " )- .)'/( " /0102#(

!

33

"

! %(

slide-8
SLIDE 8

!

"#$%%&'&( %)%#*+ !!"#!"# $ #!" ! $%# " !%

& ' ( $ )%*

& + ,%!-# $

! #

"

!%

& !"#."

  • % ! " ' /0

!"#$ !%

& !1# $ #!1# '

() *!1#2!1% ! +3%# 4!!1% ' ,- *!1##% ' !() *!1##%+ !"%$ *!1# $ !)%* &4 .!

"

!1% ' +3%

#

!1%# /0!%3 '

#

!1% %3 !

#

!1%# ! +31' $ !)%* & /

"

!1%!!1% 5 "' 3 $ "#+ !"&$ '(()*+,-./ !-67$ "8#!+ 9!2

3

$

! #

"

!%

& !"#."+

!"0$

slide-9
SLIDE 9

!!!

"

!"# " # !#$$$!% $% &%$' "! %$ # !$ &'() ! &)'** #

"

()$*))$* &'()&)'+ )** +,&)'* !"# " # !,"+ - # ! $% &%$' "! %$$

slide-10
SLIDE 10

! "#$%&'(%# )*+#&$

!!"#! " $ %#$$ " % !&#!

! !

"! '()"*#$"%$( &'(# "

+# ( #!$$ !"#$ %#,$ %&' - " %. / " %0

slide-11
SLIDE 11

!

!!! " !

!!

"

! !" #$%

""& #$'"(%

!" #$%"

!

!!

"

$& $ '()*+,-) -' & $). ' ,) )(&%/-0 &1$22 & -0 2$03" '4'"01,-) 1$&& 5"*-1"& 2$03"67) +#,& *$&" +#" 8#-+-) &8"*+0$2 '()*+,-) #$& $ 9(")*#". )'*( :#,*# ;,"2.& %$),&#1")+ -'

!

!!

"

%

!

!!

"

$& $ '()*+,-) -' & '-0 ' ! )6

!

!!

"

$& $'()*+,-) -' ' '-0 & ! )%<0,+,*$2 5"#$%,-06

slide-12
SLIDE 12

!"# !!"" # ! $%&' $% &'(%

!

((

"

! ")#"$"%&*' $&)*& '+#%%, -*&$).+%#/01,". '.'21,), 3"# ,4'22 &+#,-./ 0 ##, ! $&+5&)#'2 ,144%6#1 1#'2&7 8#%'9, :1.'4)*'221 ).6" 31#2& # 31#2& # 1#"& # 1#"& ', ). ;50<

! "#$$%&'

( )* +, )-.#/ $%001 +, 2%3, $%0002)*/1456 75&&,7/)5- %-8 %-5$%45#0 8)$,-0)5- +2)72 %&, 6%#6, )-3%&)%-/9 : 4 ! """;-74#8)-6 3%7##$ .54%&)<%/)5- +, 7%- %35)8 )-*&%&,8 8)3,&6,-7,0+ = >2,&, $%' ?, % 7&)/)7%4 75#.4)-6 *5&

!

((

"

$! $+

slide-13
SLIDE 13

! "#$%&'()*+& ,-./,".

! ! " #"#$" #$ $ " #%&#$'"#$(' $ )%*+ ! %, " *-(& " .&) $ " '/%, ! (&'0 !"#$ ! ! " #1'23%"#$" #$& " % #1'&#$'23%"#$(' " ' ((#($('& $)%*+ ! %, " *-(& " .&) $ *,#4 ! 5#4 $ " '1'/%, ! (&' !%&$ #+#0 +$$ ! '1#$0 1#$ ! /*61%"0 ""0 ""& +) %

!

7( ) ) "7(

"

0 +"0' % "*

!

7"0' ) ) "7"0'

"

+# % +# !

!

) 8 8 )

"

0 +* % +)+"+'+( !

!

) "*8 *8 )

"

+#* ! +#* ! "*+#+*0 +## ! *+#+#0 +#* ! *+#+*9 !%"$

slide-14
SLIDE 14

!"#$# %$# &'( $#)*+)%+& ,%&$-.#/ '"-." %+&-.(,,*&#/ '-&" (&"#$ &"$## ! ,%&$-.#/0 !"#$# #1-/&/ &'( 2-+)/ (3 ."-$%4 &$%+/3($,%&-(+ " ! !"#$#$!%&"% " ! !"#$$!'&"% 3($ ,%//4#// &"#($5 -+6%$-%+&0&$(& /5,,#&$5 -/ 7#+#$%&#) 85 "'%% !%% !'% !%'#( 9%// &#$, 8$#%2/ "!%% !'# /5,,#&$5 )('+ &( &$)& $ &$)& 7#+#$%&#) 85 "'%% !%'#( ) % !%' * # (+!%% !', *

!

'

  • &'

"

% )' * ) ' ) ( ( :;;< =$)-+%$5 ,%// *+"" 8$#%2/ ."-$%4 /5,,#&$50>%$-&5 6-? (4%&-+7 ,%// *,")" -/ @%$-&5 ()) 8*& /-+74#& *+)#$ ."-$%4 &$%+/3($,%&-(+0>%$-&5 &$%+/3($, -/ -( * $--% &-)% -(&(A#$# ")" -/ % /@-+ )#+/-&50 ". # (+!)% !(," * ")" * .)$-& & .*$-&( :;B<

slide-15
SLIDE 15

! " !#$ %&'("#$!$)*% !&'&!!# " !&'&( !"#$%& $'($')'*+%+#,* -#+" .%)) )" " )* " )+ ,-($* " # )./ + )0' ! ! # $ " (! # $ + )+*'+ $, ! ),

+ + ". + (! # $ + )!*'!

$, ! ),

! + ". (

/012 !"#"$ %&'()'*+',-,% .+/,'0 1'+2 34-,)5-6 )7.- 1 #) %* #*+$#*)#3 34+5,6 %*7 -' "%8' *, #*9$%$'7 7#8'$:'*3');1 #) %))4.'7 +, .,7#9< +"' %*,.5 %&,4) 7#.'*)#,* ,9 9'$.#,*; 2-

  • (3* " !"(456 ! 353673, ! "1.56873,

3, ! 1, + ". * ! "93536 3$ % /0=2 8*

  • (:* " ;(:!1,*% 80
  • (:* " #

1.(;(:!1,*!;(:*/( /0>2

slide-16
SLIDE 16

!

!"#

$!$ ! " !%#$& " ' % (& #( ' (# $' " )&# % ! ' " ) % $* ! !& )# ( !& " ' ( %# )+ (, ' " )- !"#$ %& .$%#& '( )*+( !/' " )

  • !

"

! ' " )

#

# & % *+$+$0$& ,1( $+$0$ % !&- !",$

  • . /& 234- '( .(0 *&12*314. 5/2(&./1& 4 & ! 617

8&/0( +*9442 (:;(90*0/1& +*34( 4 " %# ,1(% %#

  • #1+ & !" ( " %#/,1/$!! %#
  • #1+&" !"<$

')/9) 2*= >( 91&./.0(&0 '/0) 0)( ?*55*7 @9)'/&A(7B C=.1& (DE>= FEG*0.4=*2* H IEJ*A*)/71E%0 )*. >((& .)1'& 0)*0

$

55

%

! + /& KLM-+ 5(;(&5(&9( 16 2*.. ( 2*=

>( .2*33EN17 /&8&/0(./2*3 + 3/&(*7 *;;71:/2*0/1& )135.O'( )*+( ( " %#/,1 *. /& PQC-

slide-17
SLIDE 17

!" !"#! #"$%&"%'" ()(*%$ #$ $ " $ " %&#'$() %%&) !') !#) ***() # " +# )(, * ' )% " ') , " +#')('%' # ' )%() % $" &)

!

  • "

" ./%/0+* +,-. !"#!$"%&$' %()$ /0#$ &112'3#4&%#'" 0'56$ 7'2 $ " #,*!"*586#"9 :&*884 1'5&2#;&%#'" 78"*%#'" %0&% #$ <2#%= %(" >? 1&2#%? (:(" &"6 '66 1#(*( +12%3( " %&12#3132 3# (++%3(*/$412535+6%3() +,@. /0( (3&*% 12'1&9&%'2 #$ 9#:(" >? #12%3( " %&12 # 3132 3# # /%%3(412535 3# ( #/ 3# # +%3(* +,A. B( 0&:( & $1(*%2&5 78"*%#'" 7'2 8"C8("*0(6 *&$( %&12 # 3132'3#(5+%3( # /412535'$56%3(*

slide-18
SLIDE 18

!

!!"" #

"

#$!%&!$"! &!!$' "" $ %(!$"! (!!$' "" # )& %&!*&"""" $ )( %&!*(""""' !""# '()! ! !!""" # !*&")&!*(")(""")+ !"$# !"#$ %"& '"($& $%)#*%#)&$ ()& %"& $(+& ,-%" %"(% ./ 0#&1*"&2 *($&3 %&' ()*+,-./0 ,'12,3 4.1502 67-809 :161,1/;<-,,3 =-88;>0 (%*+ ,-./0 ,-'12,3 4.1502 67-809 %&

.!"" ?1. - # *' / #

*' ,0 # +' 12!+"+ %(

. !""' - # *' / #

*' ,0 # +' 12!+"+

slide-19
SLIDE 19

!"#$% &%'%(&%'%() )%*+, -. /"0##+ '-1"*23")2-( ! 4", " 0#) !!"!"# ! #

!

!$$ 5678 .-* # "% & $"#$%9:'%0)*"1 .#(0)2-( .*-+ )42, )%*+ /"(; 2,4%, 2( )4% 2(.*"*%&9<4#, 2) 4", (- %=%0), -( )4% 2(.*"*%& >%4"/2-#* -. $1#-( '*-'"$")-*9 ?9@2,"*,ABC :9?"- &2,0#,,%& )4% 2(.*"*%& >%4"/2-#* -. ! ") 42$4%* -*&%* "(& '-2() -#) )4% ">-/% *%,#1), 2( '%; *#)#*>")2/% ,%(,%9 !"#"$ %&'()*(+,+- .*/+(0 D) 2, %",B )- &%*2/% )4% "(-+"1-#, &2+%(,2-( 2( )4% E; 0-+'-(%() ,'2(-* 0",%9 %# % %! # %" 56F8

slide-20
SLIDE 20

!"#$# %& '( #)*$+ ,('&*$+%'*& -($ !! ! "" ##$! ! "" $"#%& ./01

! "#$$%&'

2345'%"&" ( '%'& # '%'& 678 234 ,+' 9# :';#$&*((; 9< (:$ =#"(;> ?7&@%'($A

!

))

"

( ! *+,+-"&

B7&@%'($A C(*" (-

!

))

"

! ,+' 9# D'%*# E>

F"+* ,+' 9# ;('# -($ !(@(G(H%,+GG< =+&&%I# 264 E 8:==+*%(' -($ ,&

$

#

,!"$

)*+%+,%&

slide-21
SLIDE 21

mass

slide-22
SLIDE 22

! "#$#%#&'#(

!"#$%$%&'(')*+&',-.%,%/0*12',3*$41'.+54*'$ 4' 406 406'17 '8 9+:$4*;6. 8*6)./<"=>?@3A*)67B *$461/5*6$56% !C#/%.DEDF31%GHIJKL-/%4DMNODPQR3:RRHOE QS TUVEKIE )*+,WX=B WW=<CXXX@31%GHIJKL3TFDNFKRPY54TZ"XXX<"=[C@% !\#5%G%&]F^DR3$]IODFTUVEKIE-\[><"==C@W"=BWW?32DKBKIUK 2QR^Q3 *RP%G%_Q^%TUVE%!""`>>>B[CC3"==a% !W#1%GHIJKL3)%/QOQbKDb3TUVE%1Db%+./%a<"=?[@"W[a% !a#7]KIUK 0QEUKRQ3TFQIDD^KRcE QS 5'$4*$+'+/ :.,:$56/ *$ 95. CXX[`\?"BC>X% !?#4QVQJK _HPE]VHMH30K^DJQ $HcHUKFQ3_Q^%TUVE%)DPP% :"a <CXXX@ C\>\BC\[?

slide-23
SLIDE 23

!"#$%&'() *+,-(,.+/012-)3+ $-%/*34,5$'65!"#5789:7;<=>7;5 !7#?5$5@?A?$$B C' D?EEF/BGGBE0 FH *IJ0KL0 $%&'M>9N M>;89:77<5 !:#J1+O3+ I%,3+P%/*(%O''C+PQ, %R 0O+'PO'/*%,8EL=>>7S>M:<5 !9>#L505H+,3'(/ $'+P3-() BT.%R'(/U5V-(2/*5D-(+,/*34,5$'65V">W>"X