List of errata for publications
Corrections: The r.h.s. of eq. (33) equals P/3. The decomposition of
n(a) in lemma (3.2) is only general for N=2 and the
conclussion that P is always even without twist only holds for that
case (I thank Andreas Wipf
for pointing this out). In lemma (4.1) factors 1/2 were forgotten in the
definitions of mi and ai. First line of
lemma (A.2) replace the first j for the set labels by i. Also
it is more conventional to take -P as the Pontryagin index.
Corrections: In eq. (A.2) z(N-1)/2 should be for both cases
z-(N-1)/2, whereas on the diagonal zM-1
should be zN-1
Corrections: In eq. (3) the argument of the sin needs to halved. The
integration in eq. (4) needs to run between the g dependent
Corrections: In eq. (4.13) the Airy function should be replaced by its
derivative, see also eq. (94) in 38. which
also corrects in the exponent of eq. (5.45) the power of the subleading term
Below eq. (47) one should read MS for MS-bar. At the end of App. A the sum
over a2n+1 runs from n=0
Corrections: In eq. (3.41) one derivative too many. Some signs in eqs. (4.22)
and (4.26) are wrong. In eq. (5.20) the factor -1/2 should be dropped
In eq. (8.18) replace the first factor, 4(1+i+4j), by 4i(1+i+4j).
Table I, lower part, lists norms of X, rather than P.
Eq. (8.34) applies for q=q' only. In eq. (8.35) put m=q,m'=q'
and multiply with hatN(n,q)hatN(n',q')/2. Multiply the right hand side
of eq. (8.42) with r4.
Corrections: Sign error in eq. (22), see 35.,
sect. 2. Below eq. (35) reference should have been made to eq. (6) instead
Corrections: 2N1/2 should be replaced by (2N)1/2
in eqs. (4a-c)
typos in eqs. (2.3-4), (2.6), (2.8), (2.9), (2.23), (3.12), (A.9), (B.7) and
in table 1 (alpha3 and kappa8 sign change), table 7
(energy of E+ at g=1.4 corrected). See also
27. (sect. 6) and 30.
(sect. I.2) for the issue of assigning correct quantum numbers to the
T2 and T1 glueball states (I thank Claus
Vohwinkel for pointing this out)
- Printer's error (see erratum): Wrong figure printed. Additional correction:
missing brackets in eq. (16)
- Corrections: typos in eqs. (1), (16), (25), (30), (32) and (36)
- Corrections, typo in eq. (3.7) and revision of tab. 1
- Corrections: typo in eq. (3) and alpha2 in tab. 1
- Correction: In Eq.(26) replace 2 Sqrt Trad(X) by
- Corrections: just above eqs. (2.8) a c2 missing, typos
in eqs. (3.6), (3.10), (4.23), (4.27), (4.33), (4.36), (4.40), (4.42),
(4.46), (5.1), 1st line above eqs. (2.8) and (4.46), 1st line in tab. 3
- Correction: In Eqs.(2.1) and (2.3) replace
2 Sqrt Trad(X) by Trad Sqrt(X).
Corrections: typos in eqs. (8), (16) and (17);
See also 40. for
a correction concerning sect. 3 and
a note on the non-contractible sphere argument
Corrections: typos in eqs. (69-72) and (77-79).
See also 43. at
the end of sect. 3
Corrections: In eq. (8) and the expression below eq. (7) some terms were not
listed, see 52., eq. (21) and below
Corrections: two minor typos
Corrections: typos in eqs. (31) and (41), as well as factors a half and signs
- Note added in proof in Journal version. Printer's error: in eq.(5) the
closing bracket in the third line from the bottom, should be at the end
of the line below that (i.e. both terms need to be multiplied with
pi rho2). Additional corrections: minus sign just
above and in eq.(7); in the figure the action density was cut off below
1/(2e), instead of 1/e. In eq.(20), top line, the argument
of the exponent has to change sign.
- For eq.(7), the boundary term has the opposite sign. Eq.(38), the
exponent in the Fourier series of lambda has to change sign. Furthermore,
lambda-hat-dagger(z')lambda-hat(z) has z and z'
interchanged. Eq.(76) has an overall minus sign. The result in eq. (97) is
four times too large, the overall factor two should have been a half. In
eq.(100) r and s should be interchanged. Printer's error:
In eq.(A.3) the first line, (z-z) should be replaced by (z-z').
- Corrections: Figure 1 was cut off below 1/(2e), instead of
1/e. In eq.(9) the index 3 on eta-bar and a constant term for
A0 was omitted.
- Corrections in the caption of Figure 1: the first and third mass
parameter were interchanged, they should read
second component of the position of the first consitituent had the wrong sign
and should read y1=(-1/2,-1/2,0). Finally the action was cut
off below 1/(2e), instead of 1/e.
- Corrections: Three lines below eq.(3) the mass has to be divided by 2.
Figures 1 and 3 were cut off below 1/(2e), instead of 1/e.
Figure 2 was cut off below 1/(2e2), instead of
1/e2. In the caption of figure 1 the coordinates of
the first constituent should read y1=(-1/2,-1/2,0).
- Corrections: The reference to Eq.(40) in Ref.[8b] just above eq.(16)
should be replaced by a reference to Eq.(40) in Ref.[7b], the
second paper (63.)
listed in Ref..
- The subscript z that appears in Eq.(6) for
the Greens function should be x (as in Eqs.(5) and (8)).
- In Eq.(4) the right hand side should be multiplied with 1/2.
- In Eq.(6) the index on f should be x instead of z.
Just above Eq.(9), it should have been stated that the result quoted for
SU(2) is for either z=0 (m=1), using that mu2=
-mu1=nu1/2, or z=1/2 (m=2), using that
. Eq.(9) generalizes this to arbitrary z and SU(N).
For Eq.(21) and the SU(N) result below it, the cores of the constituents
are assumed not to overlap, in which case the result is valid up to
exponentially small corrections.
- For Eqs.(13,14) the cores of the constituents are assumed not to overlap,
in which case the result is valid up to exponentially small corrections.
- Corrections (in the hep-ph version): One factor of Pi too many for the
r.h.s. of Eq. (8). In Eq.(17) and (19), and at the top of pg. 23, replace
2 Sqrt Trad(X) by Trad Sqrt(X).
Third line of sect. 3.5, "is crucial to preserve the gauge symmetry"
should read "is crucial to preserve the supersymmetry". Additional
correction: 9th line above section 6, "Beyond g(R) ~ 2.8" should read
"Beyond g(R) ~ 2.35" (or "Beyond f ~ 0.28").
- In Eq.(5) the minus sign has to be replaced by a plus.
- New results on the groundstate wave function have been added (3 Jan. 2002).
In addition correction of minor typo's, an imporved discussion around Eq.(2),
and below Eq.(10), as well as adding on pg. 8 (6th line of 2nd paragraph) a
reference to Smilga's effective Hamiltonian analysis in the supersymmetric QED
case. All corrections and additions have now been implemented for v.2 on the
Additional correction: In Eq.(23), 1st line, replace
xja by xj.
- In Eq.(13) cos(2pi t) should be cos(2pi t/beta) and in
Eq.(15) e-2pi i t should be e-2pi i t/beta.
One could also divide the righthand side of Eq.(14), and hence also the
Greens function, by beta. In that case many factors of 1/beta would then get
absorbed in the Greens function. This would have been the more natural choice
from the point of view of fourier transforming the ADHM data.
In the figure which illustrates Eq.(71), the index + and - for the
expression of Sigmam should be interchanged. It should
read, as in Eq.(71), R+m-1(mum)+
Sm+R-m(mum). (Has been
corrected in the published version).
Additional corrections: In Eq.(5), take the anti-hermitian part.
Just below Eq.(13), A-hat is of course anti-hermitian.
In Eq.(69), Rm should have been shown without
argument as in the definition. In the 2nd line below Eq.(73),
Trk should be replaced by Tr2k. In Eq.(80),
F should be replaced by script F (and the index on mu
should be m instead of n). Eq.(88) uses e.
should be -S2 (since S2=Y2-
Y1 and Rm=x-Ym,
with Ym=eYm). Hence everywhere
in Eqs.(88-90) change e to -e (or interchange
R2, r2(i) with
R1, r1(i)). The
final result remains unaffected.
- Third line below Eq.(23), mu should have an index m in
the expression for fm. In Eq.(39) an overall factor
Abs(zeta) should be inserted and in the line below this equation the
weight factor has to be conjugated. In Eq.(78) a term 2(k
x3|x|)2 was lost in the typesetting. All these
corrections have been implemented in the published version.
Additional corrections: For the 2nd line below Eq.(3)
zmu should strictly speaking be replaced by
z deltamu0. In writing Eq.(28) we should have specified that
z' has to be bigger or equal to z and valid up to and including
the boundaries of the interval on which it is defined. (When z' is
smaller than z, simply interchange z and z' -- in this
limit the function is real). Eq.(61) should read D2=4
(c3-c2) instead of D2=(c3
-c2)/4. Just above Eq.(67) it should have read that
alpha2=-alpha1=alpha/(4 Pi), instead of
alpha/Pi. In Eq.(68) the indentity matrix is of course 2X2
(and not 1X1). From Eq.(71) until (but not including) Eq.(72) there
were three instances where a factor pi in front of rho2 was
In Appendix A we should have defined more
explictely that Fm (so without the z-dependence
specified) stands for Fm(mum+1).
- In Eq.(28) a factor a half is missing in front of the commutator term.
- Corrections implemented in the published version, and in v2 on the
archive: In Eq.(38) a factor i was forgotten for the term with
the Jacobi elliptic functions. In the captions of figures 1, 3 and 4,
the scales of the zero-mode densities are enhanced by an additional factor
2pi2. Some factors of 2pi were also forgotten in quoting the
time dependent values of the action density in the second paragraph above
Additional corrections: In the second identity of Eq.(29) a sign on the rhs
should be inserted. In footnote (4) we used (d/dz)det(Y)=Tr(Y-1
dY/dz) det(Y), but forgot to write the det(Y) factor. It does not affect the
result since the Nahm equation implies Tr(Y-1dY/dz)=0. Using the
already established fact that det(Y) is conserved would have been easier at